200:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Composición de funciones :@0.404235:0.110915:0.724373:0.110915:0.724373:0.066256:0.404235:0.066256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y funciones inversas:@0.404235:0.148634:0.648685:0.148634:0.648685:0.103975:0.404235:0.103975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.23. Reconocer funciones inyectivas, sobreyectivas y biyectivas para calcular la función inversa (de funciones biyectivas), comprobándola mediante la composición de funciones.:@0.143847:0.943686:0.873690:0.943686:0.873690:0.933644:0.143847:0.933644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.24. Resolver y plantear aplicaciones de la composición de funciones reales en problemas reales o hipotéticos.:@0.143847:0.952487:0.636383:0.952487:0.636383:0.942445:0.143847:0.942445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.101454:0.307805:0.101454:0.307805:0.085981:0.199646:0.085981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una función :@0.199884:0.130082:0.336910:0.130082:0.336910:0.115019:0.199884:0.115019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biyectiva?:@0.153341:0.145924:0.216172:0.145924:0.216172:0.130861:0.153341:0.130861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.193455:0.363493:0.193455:0.363493:0.177983:0.199646:0.177983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo representas en :@0.199884:0.222083:0.347620:0.222083:0.347620:0.207020:0.199884:0.207020:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un diagrama de Venn la com-:@0.153341:0.237925:0.345635:0.237925:0.345635:0.222862:0.153341:0.222862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
posición de funciones?:@0.153341:0.253767:0.301025:0.253767:0.301025:0.238704:0.153341:0.238704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.176848:0.482316:0.176848:0.482316:0.159902:0.404236:0.159902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,  ,   tres conjuntos no vacíos cualesquiera,   una fun-:@0.482068:0.176385:0.891741:0.176385:0.891741:0.159887:0.482068:0.159887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.523546:0.176501:0.564870:0.176501:0.564870:0.160032:0.523546:0.160032:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.826317:0.176501:0.830613:0.176501:0.830613:0.160032:0.826317:0.160032:0.000000
ción de   en  ,   una función de   en  . La composición de la función :@0.404217:0.193736:0.895939:0.193736:0.895939:0.177238:0.404217:0.177238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.460337:0.193851:0.471607:0.193851:0.471607:0.177383:0.460337:0.177383:0.000000
B g:@0.497268:0.193851:0.520579:0.193851:0.520579:0.177383:0.497268:0.177383:0.000000:0.000000:0.000000
B:@0.634839:0.193851:0.644029:0.193851:0.644029:0.177383:0.634839:0.177383:0.000000
C:@0.669673:0.193851:0.679710:0.193851:0.679710:0.177383:0.669673:0.177383:0.000000
g:@0.404236:0.211202:0.411673:0.211202:0.411673:0.194733:0.404236:0.194733:0.000000
 con la de  , que se nota :@0.411422:0.211086:0.576755:0.211086:0.576755:0.194589:0.411422:0.194589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.481702:0.211202:0.485998:0.211202:0.485998:0.194733:0.481702:0.194733:0.000000
g   f:@0.576504:0.211202:0.602900:0.211202:0.602900:0.194733:0.576504:0.194733:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.587584:0.211376:0.593999:0.211376:0.593999:0.197929:0.587584:0.197929:0.000000
, es la función de   en   definida como::@0.602649:0.211086:0.873461:0.211086:0.873461:0.194589:0.602649:0.194589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.720225:0.211202:0.731495:0.211202:0.731495:0.194733:0.720225:0.194733:0.000000
C:@0.756078:0.211202:0.766115:0.211202:0.766115:0.194733:0.756078:0.194733:0.000000
(:@0.548803:0.235565:0.554756:0.235565:0.554756:0.219068:0.548803:0.219068:0.000000
g   f x:@0.554756:0.235681:0.601532:0.235681:0.601532:0.219212:0.554756:0.219212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.566334:0.235855:0.572749:0.235855:0.572749:0.222408:0.566334:0.222408:0.000000
)( ) = ( ( ( )),       :@0.582151:0.235565:0.732708:0.235565:0.732708:0.219067:0.582151:0.219068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f x:@0.632529:0.235681:0.663643:0.235681:0.663643:0.219212:0.632529:0.219212:0.000000:0.000000:0.000000:0.000000:0.000000
∀:@0.690716:0.243151:0.702288:0.243151:0.702288:0.224152:0.690716:0.224152:0.000000
x:@0.702297:0.235680:0.709771:0.235680:0.709771:0.219212:0.702297:0.219212:0.000000
:@0.713913:0.235046:0.728565:0.235046:0.728565:0.221673:0.713913:0.221673:0.000000
A.:@0.732708:0.235680:0.747215:0.235680:0.747215:0.219212:0.732708:0.219212:0.000000:0.000000
De la definición se tiene :@0.404235:0.270266:0.578621:0.270266:0.578621:0.253769:0.404235:0.253769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.578621:0.270382:0.606020:0.270382:0.606020:0.253913:0.578621:0.253913:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.590203:0.270555:0.596618:0.270555:0.596618:0.257109:0.590203:0.257109:0.000000
:  :@0.606020:0.270266:0.617059:0.270266:0.617059:0.253769:0.606020:0.253769:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.404235:0.314395:0.534890:0.314395:0.534890:0.297608:0.404235:0.297608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.404235:0.331587:0.420592:0.331587:0.420592:0.314872:0.404235:0.314872:0.000000:0.000000:0.000000
Sean   = {–30, –25, –20, –15},   = {0, 1, 2, 3, 4},:@0.427970:0.331370:0.758215:0.331370:0.758215:0.314872:0.427970:0.314872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.465769:0.331486:0.477039:0.331486:0.477039:0.315017:0.465769:0.315017:0.000000
B:@0.645398:0.331486:0.654587:0.331486:0.654587:0.315017:0.645398:0.315017:0.000000
 :@0.404235:0.348721:0.408377:0.348721:0.408377:0.332223:0.404235:0.332223:0.000000
C:@0.427970:0.348836:0.438007:0.348836:0.438007:0.332368:0.427970:0.332368:0.000000
 = {10, 20, 30, 40, 50},   y   son las funciones que se muestran en :@0.438007:0.348721:0.895842:0.348721:0.895842:0.332223:0.438007:0.332223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.591089:0.348836:0.619737:0.348836:0.619737:0.332368:0.591089:0.332368:0.000000:0.000000:0.000000
los siguientes diagramas de Venn-Euler: :@0.427970:0.366071:0.709299:0.366071:0.709299:0.349574:0.427970:0.349574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404235:0.487527:0.408377:0.487527:0.408377:0.471029:0.404235:0.471029:0.000000
La función :@0.427970:0.487527:0.504817:0.487527:0.504817:0.471029:0.427970:0.471029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.503912:0.487642:0.529132:0.487642:0.529132:0.471174:0.503912:0.471174:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.514413:0.487816:0.520829:0.487816:0.520829:0.474369:0.514413:0.474369:0.000000
 está definida del modo que se indica a continuación::@0.528939:0.487527:0.891700:0.487527:0.891700:0.471029:0.528939:0.471029:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404216:0.516951:0.408358:0.516951:0.408358:0.500453:0.404216:0.500453:0.000000
g   f:@0.427951:0.517066:0.455346:0.517066:0.455346:0.500598:0.427951:0.500598:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.439529:0.517240:0.445945:0.517240:0.445945:0.503793:0.439529:0.503793:0.000000
(–30) =  ( (–30)) =  (4) = 20,:@0.455346:0.516951:0.662640:0.516951:0.662640:0.500453:0.455346:0.500453:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.513835:0.517066:0.531521:0.517066:0.531521:0.500598:0.513835:0.500598:0.000000:0.000000:0.000000
g:@0.595963:0.517066:0.603400:0.517066:0.603400:0.500598:0.595963:0.500598:0.000000
 :@0.404216:0.534301:0.408358:0.534301:0.408358:0.517804:0.404216:0.517804:0.000000
g   f:@0.427951:0.534417:0.455346:0.534417:0.455346:0.517948:0.427951:0.517948:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.439529:0.534591:0.445945:0.534591:0.445945:0.521144:0.439529:0.521144:0.000000
(–25) =  ( (–25)) =  (2) = 60,:@0.455346:0.534301:0.662640:0.534301:0.662640:0.517804:0.455346:0.517804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.513835:0.534417:0.531521:0.534417:0.531521:0.517948:0.513835:0.517948:0.000000:0.000000:0.000000
g:@0.595963:0.534417:0.603400:0.534417:0.603400:0.517948:0.595963:0.517948:0.000000
 :@0.404216:0.551652:0.408358:0.551652:0.408358:0.535154:0.404216:0.535154:0.000000
g   f:@0.427951:0.551768:0.455346:0.551768:0.455346:0.535299:0.427951:0.535299:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.439529:0.551941:0.445945:0.551941:0.445945:0.538494:0.439529:0.538494:0.000000
(–20) =  ( (–20)) =  (0) = 40,:@0.455346:0.551652:0.662640:0.551652:0.662640:0.535154:0.455346:0.535154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.513835:0.551768:0.531521:0.551768:0.531521:0.535299:0.513835:0.535299:0.000000:0.000000:0.000000
g:@0.595963:0.551768:0.603400:0.551768:0.603400:0.535299:0.595963:0.535299:0.000000
 :@0.404216:0.569003:0.408358:0.569003:0.408358:0.552505:0.404216:0.552505:0.000000
g   f:@0.427951:0.569119:0.455346:0.569119:0.455346:0.552650:0.427951:0.552650:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.439529:0.569292:0.445945:0.569292:0.445945:0.555845:0.439529:0.555845:0.000000
(–15) =  ( (–15)) =  (3) = 30.:@0.455346:0.569003:0.662640:0.569003:0.662640:0.552505:0.455346:0.552505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.513835:0.569119:0.531521:0.569119:0.531521:0.552650:0.513835:0.552650:0.000000:0.000000:0.000000
g:@0.595963:0.569119:0.603400:0.569119:0.603400:0.552650:0.595963:0.552650:0.000000
 :@0.404216:0.598427:0.408358:0.598427:0.408358:0.581929:0.404216:0.581929:0.000000
En la Figura 6.1., se muestran los resultados de la función :@0.427951:0.598427:0.830917:0.598427:0.830917:0.581929:0.427951:0.581929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.830917:0.598543:0.857547:0.598543:0.857547:0.582074:0.830917:0.582074:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.842115:0.598716:0.848531:0.598716:0.848531:0.585269:0.842115:0.585269:0.000000
.:@0.857354:0.598427:0.860109:0.598427:0.860109:0.581929:0.857354:0.581929:0.000000
Ejercicios resueltos:@0.404216:0.633504:0.534871:0.633504:0.534871:0.616717:0.404216:0.616717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.404216:0.650696:0.416488:0.650696:0.416488:0.633981:0.404216:0.633981:0.000000:0.000000
  Sean   = {1, 2, 3, 4},   =   =  . Consideremos las funciones  ,   :@0.416488:0.650479:0.895885:0.650479:0.895885:0.633981:0.416488:0.633981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.467406:0.650595:0.478676:0.650595:0.478676:0.634126:0.467406:0.634126:0.000000
B:@0.580994:0.650595:0.590184:0.650595:0.590184:0.634126:0.580994:0.634126:0.000000
C:@0.612589:0.650595:0.622626:0.650595:0.622626:0.634126:0.612589:0.634126:0.000000
A:@0.645032:0.650595:0.656302:0.650595:0.656302:0.634126:0.645032:0.634126:0.000000
f g:@0.871531:0.650595:0.891743:0.650595:0.891743:0.634126:0.871531:0.634126:0.000000:0.000000:0.000000
definidas como sigue::@0.427951:0.667830:0.581050:0.667830:0.581050:0.651332:0.427951:0.651332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404216:0.685181:0.408358:0.685181:0.408358:0.668683:0.404216:0.668683:0.000000
f:@0.427951:0.685296:0.432247:0.685296:0.432247:0.668828:0.427951:0.668828:0.000000
(1) = 2,     (2) = 3,     (3) = 4,     (4) = 1,:@0.432247:0.685181:0.697819:0.685181:0.697819:0.668683:0.432247:0.668683:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.499560:0.685296:0.503856:0.685296:0.503856:0.668828:0.499560:0.668828:0.000000
f:@0.571169:0.685296:0.575465:0.685296:0.575465:0.668828:0.571169:0.668828:0.000000
f:@0.642778:0.685296:0.647074:0.685296:0.647074:0.668828:0.642778:0.668828:0.000000
 :@0.404216:0.702531:0.408358:0.702531:0.408358:0.686034:0.404216:0.686034:0.000000
g:@0.427951:0.702647:0.435387:0.702647:0.435387:0.686178:0.427951:0.686178:0.000000
(1) = 3,     (2) = 4,     (3) = 1,     (4) = 2.:@0.435387:0.702531:0.710380:0.702531:0.710380:0.686034:0.435387:0.686034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.502700:0.702647:0.510136:0.702647:0.510136:0.686178:0.502700:0.686178:0.000000
g:@0.577449:0.702647:0.584886:0.702647:0.584886:0.686178:0.577449:0.686178:0.000000
g:@0.652198:0.702647:0.659635:0.702647:0.659635:0.686178:0.652198:0.686178:0.000000
 :@0.404216:0.731955:0.408358:0.731955:0.408358:0.715458:0.404216:0.715458:0.000000
Claramente, las funciones  ,   son inyectivas, sobreyectivas, biyec-:@0.427951:0.731955:0.891743:0.731955:0.891743:0.715458:0.427951:0.715458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.615342:0.732071:0.634667:0.732071:0.634667:0.715602:0.615342:0.715602:0.000000:0.000000:0.000000
tivas. Determinemos la función :@0.427951:0.749306:0.653177:0.749306:0.653177:0.732808:0.427951:0.732808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.653177:0.749422:0.679806:0.749422:0.679806:0.732953:0.653177:0.732953:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.664374:0.749595:0.670789:0.749595:0.670789:0.736148:0.664374:0.736148:0.000000
. Tenemos: :@0.679613:0.749306:0.758367:0.749306:0.758367:0.732808:0.679613:0.732808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.427951:0.778730:0.433904:0.778730:0.433904:0.762232:0.427951:0.762232:0.000000
g   f:@0.433904:0.778846:0.461299:0.778846:0.461299:0.762377:0.433904:0.762377:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.445482:0.779019:0.451898:0.779019:0.451898:0.765572:0.445482:0.765572:0.000000
)(1) =  ( (1)) =  (2) = 4,   (:@0.461299:0.778730:0.646438:0.778730:0.646438:0.762232:0.461299:0.762232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.506746:0.778846:0.524431:0.778846:0.524431:0.762377:0.506746:0.762377:0.000000:0.000000:0.000000
g:@0.569878:0.778846:0.577314:0.778846:0.577314:0.762377:0.569878:0.762377:0.000000
g   f:@0.646438:0.778846:0.673833:0.778846:0.673833:0.762377:0.646438:0.762377:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.658017:0.779019:0.664432:0.779019:0.664432:0.765572:0.658017:0.765572:0.000000
)(2) =  ( (2)) =  (3) = 1,:@0.673833:0.778730:0.840593:0.778730:0.840593:0.762232:0.673833:0.762232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.719280:0.778846:0.736966:0.778846:0.736966:0.762377:0.719280:0.762377:0.000000:0.000000:0.000000
g:@0.782412:0.778846:0.789849:0.778846:0.789849:0.762377:0.782412:0.762377:0.000000
(:@0.427951:0.796081:0.433904:0.796081:0.433904:0.779583:0.427951:0.779583:0.000000
g   f:@0.433904:0.796197:0.461299:0.796197:0.461299:0.779728:0.433904:0.779728:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.445482:0.796370:0.451898:0.796370:0.451898:0.782923:0.445482:0.782923:0.000000
)(3) =  ( (3)) =  (4) = 2,   (:@0.461299:0.796081:0.646438:0.796081:0.646438:0.779583:0.461299:0.779583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.506746:0.796197:0.524431:0.796197:0.524431:0.779728:0.506746:0.779728:0.000000:0.000000:0.000000
g:@0.569878:0.796197:0.577314:0.796197:0.577314:0.779728:0.569878:0.779728:0.000000
g   f:@0.646438:0.796197:0.673833:0.796197:0.673833:0.779728:0.646438:0.779728:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.658017:0.796370:0.664432:0.796370:0.664432:0.782923:0.658017:0.782923:0.000000
)(4) =  ( (4)) =  (1) = 3.:@0.673833:0.796081:0.840593:0.796081:0.840593:0.779583:0.673833:0.779583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f:@0.719280:0.796197:0.736966:0.796197:0.736966:0.779728:0.719280:0.779728:0.000000:0.000000:0.000000
g:@0.782412:0.796197:0.789849:0.796197:0.789849:0.779728:0.782412:0.779728:0.000000
 :@0.404216:0.825505:0.408358:0.825505:0.408358:0.809007:0.404216:0.809007:0.000000
Observamos que :@0.427951:0.825505:0.553828:0.825505:0.553828:0.809007:0.427951:0.809007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.553944:0.825621:0.580801:0.825621:0.580801:0.809152:0.553944:0.809152:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.565254:0.825794:0.571670:0.825794:0.571670:0.812347:0.565254:0.812347:0.000000
 es inyectiva, sobreyectiva, biyectiva. ¿Cómo :@0.580609:0.825505:0.895898:0.825505:0.895898:0.809007:0.580609:0.809007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
está definida la función compuesta :@0.427951:0.842856:0.681709:0.842856:0.681709:0.826358:0.427951:0.826358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   g:@0.681709:0.842971:0.708337:0.842971:0.708337:0.826503:0.681709:0.826503:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.689766:0.843145:0.696181:0.843145:0.696181:0.829698:0.689766:0.829698:0.000000
?, ¿es :@0.708145:0.842856:0.744997:0.842856:0.744997:0.826358:0.708145:0.826358:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f   g g   f:@0.744997:0.842971:0.817148:0.842971:0.817148:0.826503:0.744997:0.826503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.753052:0.843145:0.759467:0.843145:0.759467:0.829698:0.753052:0.829698:0.000000
 = :@0.771431:0.842856:0.790523:0.842856:0.790523:0.826358:0.771431:0.826358:0.000000:0.000000:0.000000
:@0.801716:0.843145:0.808131:0.843145:0.808131:0.829698:0.801716:0.829698:0.000000
?:@0.816955:0.842856:0.822657:0.842856:0.822657:0.826358:0.816955:0.826358:0.000000
3.:@0.404216:0.872496:0.416488:0.872496:0.416488:0.855782:0.404216:0.855782:0.000000:0.000000
  Sean  ,   las funciones definidas de   en   que se especifican:@0.416488:0.872280:0.868907:0.872262:0.868907:0.855764:0.416488:0.855782:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u v:@0.465749:0.872395:0.489446:0.872395:0.489446:0.855927:0.465749:0.855927:0.000000:0.000000:0.000000
Q:@0.679714:0.871175:0.695064:0.871175:0.695064:0.858313:0.679714:0.858313:0.000000
Q:@0.720898:0.871175:0.736249:0.871175:0.736249:0.858313:0.720898:0.858313:0.000000
 :@0.404231:0.896741:0.408373:0.896741:0.408373:0.880243:0.404231:0.880243:0.000000
a continuación:  ( ) =   + 1,     ( ) = –     – 1,        .:@0.427966:0.896741:0.826294:0.896742:0.826294:0.880244:0.427966:0.880243:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u x:@0.541456:0.896857:0.564092:0.896857:0.564092:0.880388:0.541456:0.880388:0.000000:0.000000:0.000000
x:@0.589137:0.896857:0.596612:0.896857:0.596612:0.880388:0.589137:0.880388:0.000000
2:@0.596626:0.890389:0.601579:0.890389:0.601579:0.880771:0.596626:0.880771:0.000000
v x:@0.648489:0.896857:0.669700:0.896857:0.669700:0.880389:0.648489:0.880389:0.000000:0.000000:0.000000
∀:@0.766197:0.904328:0.777769:0.904328:0.777769:0.885329:0.766197:0.885329:0.000000
x:@0.777778:0.896857:0.785253:0.896857:0.785253:0.880389:0.777778:0.880389:0.000000
:@0.789394:0.896223:0.804046:0.896223:0.804046:0.882850:0.789394:0.882850:0.000000
Q:@0.808188:0.895655:0.823539:0.895655:0.823539:0.882793:0.808188:0.882793:0.000000
 :@0.404230:0.921221:0.408372:0.921221:0.408372:0.904723:0.404230:0.904723:0.000000
Determinemos las funciones compuestas      y  :@0.427965:0.921221:0.781714:0.921221:0.781714:0.904723:0.427965:0.904723:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v  u:@0.725241:0.921336:0.757517:0.921336:0.757517:0.904868:0.725241:0.904868:0.000000:0.000000:0.000000:0.000000
:@0.736787:0.921510:0.743203:0.921510:0.743203:0.908063:0.736787:0.908063:0.000000
u   v:@0.781714:0.921336:0.813790:0.921336:0.813790:0.904868:0.781714:0.904868:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.794679:0.921510:0.801095:0.921510:0.801095:0.908063:0.794679:0.908063:0.000000
.:@0.813598:0.921221:0.816353:0.921221:0.816353:0.904723:0.813598:0.904723:0.000000
A:@0.631483:0.265319:0.642753:0.265319:0.642753:0.248850:0.631483:0.248850:0.000000
    ,:@0.642753:0.265203:0.680552:0.265203:0.680552:0.248705:0.642753:0.248705:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.646895:0.273302:0.663040:0.273302:0.663040:0.253439:0.646895:0.253439:0.000000
C:@0.667182:0.265319:0.677219:0.265319:0.677219:0.248850:0.667182:0.248850:0.000000
x:@0.631483:0.282670:0.638958:0.282670:0.638958:0.266201:0.631483:0.266201:0.000000
   (:@0.638958:0.282554:0.669340:0.282554:0.669340:0.266056:0.638958:0.266056:0.000000:0.000000:0.000000:0.000000
→:@0.643100:0.290653:0.659245:0.290653:0.659245:0.270790:0.643100:0.270790:0.000000
g   f x:@0.669340:0.282670:0.716116:0.282670:0.716116:0.266201:0.669340:0.266201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.680918:0.282843:0.687333:0.282843:0.687333:0.269396:0.680918:0.269396:0.000000
)( ) =  ( ( )).:@0.696735:0.282554:0.786935:0.282554:0.786935:0.266056:0.696735:0.266056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g f x:@0.741160:0.282670:0.772274:0.282670:0.772274:0.266201:0.741160:0.266201:0.000000:0.000000:0.000000:0.000000:0.000000
–30:@0.479851:0.403559:0.504952:0.403559:0.504952:0.388496:0.479851:0.388496:0.000000:0.000000:0.000000
–25:@0.479851:0.419401:0.504952:0.419401:0.504952:0.404338:0.479851:0.404338:0.000000:0.000000:0.000000
–20:@0.479851:0.435243:0.504952:0.435243:0.504952:0.420180:0.479851:0.420180:0.000000:0.000000:0.000000
–15:@0.479851:0.451085:0.504952:0.451085:0.504952:0.436022:0.479851:0.436022:0.000000:0.000000:0.000000
0:@0.576614:0.399665:0.584371:0.399665:0.584371:0.384601:0.576614:0.384601:0.000000
1:@0.576614:0.413500:0.584371:0.413500:0.584371:0.398437:0.576614:0.398437:0.000000
2:@0.576614:0.427335:0.584371:0.427335:0.584371:0.412272:0.576614:0.412272:0.000000
3:@0.576614:0.441171:0.584371:0.441171:0.584371:0.426107:0.576614:0.426107:0.000000
4:@0.576614:0.455006:0.584371:0.455006:0.584371:0.439943:0.576614:0.439943:0.000000
0:@0.740483:0.399691:0.748240:0.399691:0.748240:0.384628:0.740483:0.384628:0.000000
1:@0.740483:0.413526:0.748240:0.413526:0.748240:0.398463:0.740483:0.398463:0.000000
2:@0.740483:0.427362:0.748240:0.427362:0.748240:0.412299:0.740483:0.412299:0.000000
3:@0.740483:0.441197:0.748240:0.441197:0.748240:0.426134:0.740483:0.426134:0.000000
4:@0.740483:0.455032:0.748240:0.455032:0.748240:0.439969:0.740483:0.439969:0.000000
10:@0.824686:0.394212:0.840201:0.394212:0.840201:0.379149:0.824686:0.379149:0.000000:0.000000
20:@0.824686:0.407163:0.840201:0.407163:0.840201:0.392100:0.824686:0.392100:0.000000:0.000000
30:@0.824686:0.420114:0.840201:0.420114:0.840201:0.405051:0.824686:0.405051:0.000000:0.000000
40:@0.824686:0.433065:0.840201:0.433065:0.840201:0.418002:0.824686:0.418002:0.000000:0.000000
50:@0.824686:0.446016:0.840201:0.446016:0.840201:0.430952:0.824686:0.430952:0.000000:0.000000
60:@0.824686:0.458966:0.840201:0.458966:0.840201:0.443903:0.824686:0.443903:0.000000:0.000000
x:@0.710904:0.889725:0.718379:0.889725:0.718379:0.873256:0.710904:0.873256:0.000000
3:@0.710384:0.905948:0.718880:0.905948:0.718880:0.889450:0.710384:0.889450:0.000000
A:@0.446893:0.391586:0.457183:0.391586:0.457183:0.376549:0.446893:0.376549:0.000000
B:@0.699802:0.391586:0.708193:0.391586:0.708193:0.376549:0.699802:0.376549:0.000000
B:@0.616021:0.391586:0.624411:0.391586:0.624411:0.376549:0.616021:0.376549:0.000000
C:@0.867593:0.405844:0.876758:0.405844:0.876758:0.390807:0.867593:0.390807:0.000000
f:@0.534474:0.391586:0.538396:0.391586:0.538396:0.376549:0.534474:0.376549:0.000000
f:@0.786433:0.391586:0.790355:0.391586:0.790355:0.376549:0.786433:0.376549:0.000000
–30:@0.200825:0.503258:0.225926:0.503258:0.225926:0.488195:0.200825:0.488195:0.000000:0.000000:0.000000
–25:@0.200825:0.519100:0.225926:0.519100:0.225926:0.504037:0.200825:0.504037:0.000000:0.000000:0.000000
–20:@0.200825:0.534942:0.225926:0.534942:0.225926:0.519879:0.200825:0.519879:0.000000:0.000000:0.000000
–15:@0.200825:0.550784:0.225926:0.550784:0.225926:0.535721:0.200825:0.535721:0.000000:0.000000:0.000000
10:@0.293701:0.494650:0.309215:0.494650:0.309215:0.479587:0.293701:0.479587:0.000000:0.000000
20:@0.293701:0.507601:0.309215:0.507601:0.309215:0.492538:0.293701:0.492538:0.000000:0.000000
30:@0.293701:0.520552:0.309215:0.520552:0.309215:0.505489:0.293701:0.505489:0.000000:0.000000
40:@0.293701:0.533503:0.309215:0.533503:0.309215:0.518440:0.293701:0.518440:0.000000:0.000000
50:@0.293701:0.546454:0.309215:0.546454:0.309215:0.531391:0.293701:0.531391:0.000000:0.000000
60:@0.293701:0.559405:0.309215:0.559405:0.309215:0.544342:0.293701:0.544342:0.000000:0.000000
A:@0.167862:0.491297:0.178152:0.491297:0.178152:0.476261:0.167862:0.476261:0.000000
C:@0.336603:0.503773:0.345767:0.503773:0.345767:0.488736:0.336603:0.488736:0.000000
g   f:@0.245099:0.491297:0.269731:0.491285:0.269731:0.476248:0.245099:0.476261:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.255329:0.491670:0.261466:0.491670:0.261466:0.478808:0.255329:0.478808:0.000000
p:@0.143847:0.583405:0.155327:0.583405:0.155327:0.573381:0.143847:0.573381:0.000000
 :@0.155327:0.584113:0.158209:0.584113:0.158209:0.572636:0.155327:0.572636:0.000000
Figura 6.1.:@0.158209:0.584113:0.206777:0.584113:0.206777:0.572636:0.158209:0.572636:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.621696:0.297267:0.621696:0.297267:0.606223:0.199644:0.606223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199644:0.634264:0.283707:0.634264:0.283707:0.618791:0.199644:0.618791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Teorema:@0.199880:0.659161:0.260793:0.659161:0.260793:0.643688:0.199880:0.643688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,  ,   :@0.260759:0.658738:0.345332:0.658738:0.345332:0.643675:0.260759:0.643675:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.301322:0.658844:0.341550:0.658844:0.341550:0.643807:0.301322:0.643807:0.000000:0.000000:0.000000:0.000000:0.000000
tres conjuntos no vacíos,   una :@0.153337:0.674580:0.352421:0.674580:0.352421:0.659517:0.153337:0.659517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.316464:0.674686:0.320386:0.674686:0.320386:0.659649:0.316464:0.659649:0.000000
función de   en  ,   una fun-:@0.153337:0.690422:0.340970:0.690422:0.340970:0.675359:0.153337:0.675359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.227020:0.690528:0.237310:0.690528:0.237310:0.675491:0.227020:0.675491:0.000000
B g:@0.260724:0.690528:0.282096:0.690528:0.282096:0.675491:0.260724:0.675491:0.000000:0.000000:0.000000
ción de   en  . Entonces,:@0.153337:0.706264:0.314108:0.706264:0.314108:0.691201:0.153337:0.691201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.205140:0.706370:0.213530:0.706370:0.213530:0.691333:0.205140:0.691333:0.000000
C:@0.236943:0.706370:0.246107:0.706370:0.246107:0.691333:0.236943:0.691333:0.000000
i.:@0.153337:0.730186:0.160285:0.730186:0.160285:0.714925:0.153337:0.714925:0.000000:0.000000
  Si  ,   son inyectivas, :@0.160285:0.729988:0.302462:0.729988:0.302462:0.714925:0.160285:0.714925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.184524:0.730093:0.201534:0.730093:0.201534:0.715057:0.184524:0.715057:0.000000:0.000000:0.000000
g   f:@0.302462:0.730093:0.327088:0.730094:0.327088:0.715057:0.302462:0.715057:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.312686:0.730479:0.318822:0.730479:0.318822:0.717617:0.312686:0.717617:0.000000
 :@0.327088:0.729988:0.330870:0.729988:0.330870:0.714925:0.327088:0.714925:0.000000
es inyectiva.:@0.169956:0.745830:0.247315:0.745830:0.247315:0.730767:0.169956:0.730767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii.:@0.153334:0.769752:0.164169:0.769752:0.164169:0.754491:0.153334:0.754491:0.000000:0.000000:0.000000
 Si  ,   son sobreyectivas, :@0.164169:0.769554:0.326205:0.769554:0.326205:0.754491:0.164169:0.754491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.184521:0.769659:0.201530:0.769659:0.201530:0.754623:0.184521:0.754623:0.000000:0.000000:0.000000
g   f:@0.326205:0.769659:0.350833:0.769661:0.350833:0.754625:0.326205:0.754623:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.336431:0.770047:0.342567:0.770047:0.342567:0.757184:0.336431:0.757184:0.000000
 :@0.350833:0.769556:0.354615:0.769556:0.354615:0.754492:0.350833:0.754492:0.000000
es sobreyectiva.:@0.169972:0.786150:0.271076:0.786150:0.271076:0.771087:0.169972:0.771087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iii.:@0.153350:0.810071:0.168073:0.810071:0.168073:0.794810:0.153350:0.794810:0.000000:0.000000:0.000000:0.000000
 Si  ,   son biyectivas, :@0.168073:0.809873:0.302562:0.809873:0.302562:0.794810:0.168073:0.794810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f g:@0.184537:0.809979:0.201546:0.809979:0.201546:0.794942:0.184537:0.794942:0.000000:0.000000:0.000000
g   f:@0.302562:0.809979:0.327175:0.809982:0.327175:0.794945:0.302562:0.794942:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.312773:0.810367:0.318910:0.810367:0.318910:0.797505:0.312773:0.797505:0.000000
 :@0.327175:0.809876:0.330957:0.809876:0.330957:0.794813:0.327175:0.794813:0.000000
es biyectiva.:@0.169956:0.825718:0.247401:0.825718:0.247401:0.810655:0.169956:0.810655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
iv.:@0.153333:0.849639:0.167212:0.849639:0.167212:0.834378:0.153333:0.834378:0.000000:0.000000:0.000000
 Si :@0.167212:0.849441:0.184520:0.849441:0.184520:0.834378:0.167212:0.834378:0.000000:0.000000:0.000000:0.000000
g   f:@0.184520:0.849547:0.209149:0.849548:0.209149:0.834511:0.184520:0.834510:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.194747:0.849933:0.200884:0.849933:0.200884:0.837071:0.194747:0.837071:0.000000
 es inyectiva, :@0.208974:0.849442:0.293898:0.849442:0.293898:0.834379:0.208974:0.834379:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.169959:0.865390:0.173882:0.865390:0.173882:0.850353:0.169959:0.850353:0.000000
 es inyectiva.:@0.173706:0.865284:0.254847:0.865284:0.254847:0.850221:0.173706:0.850221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v.:@0.153336:0.889205:0.163398:0.889205:0.163398:0.873944:0.153336:0.873944:0.000000:0.000000
  Si :@0.163398:0.889007:0.184523:0.889007:0.184523:0.873944:0.163398:0.873944:0.000000:0.000000:0.000000:0.000000:0.000000
g   f:@0.184523:0.889113:0.209149:0.889115:0.209149:0.874078:0.184523:0.874076:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.194747:0.889500:0.200884:0.889500:0.200884:0.876638:0.194747:0.876638:0.000000
 es sobreyectiva, :@0.208974:0.889009:0.317645:0.889009:0.317645:0.873946:0.208974:0.873946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g:@0.169959:0.904957:0.176749:0.904957:0.176749:0.889920:0.169959:0.889920:0.000000
 es sobreyectiva.:@0.176573:0.904851:0.281460:0.904851:0.281460:0.889788:0.176573:0.889788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000