33:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.522009:0.043661:0.926913:0.043661:0.926913:0.024916:0.522009:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 EBC 11. Comprende el concepto de función real de variable real.:@0.079431:0.971366:0.417101:0.971366:0.417101:0.959939:0.079431:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si una función de en es tal que :@0.073089:0.136836:0.359524:0.136836:0.359524:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.189183:0.136836:0.193877:0.136836:0.193877:0.121401:0.189183:0.121401:0.000000 A:@0.224765:0.136836:0.234649:0.136836:0.234649:0.121401:0.224765:0.121401:0.000000 B:@0.265389:0.136836:0.274225:0.136836:0.274225:0.121401:0.265389:0.121401:0.000000 Rec f:@0.361181:0.136836:0.395860:0.136836:0.395860:0.121401:0.361181:0.121401:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) es un subconjunto propio de , no es :@0.386086:0.136836:0.710348:0.136836:0.710348:0.121124:0.386086:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B f :@0.636940:0.136836:0.663207:0.136836:0.663207:0.121401:0.636940:0.121401:0.000000:0.000000:0.000000:0.000000 sobreyectiva.:@0.073070:0.153478:0.167932:0.153478:0.167932:0.137765:0.073070:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejercicios resueltos:@0.073070:0.176915:0.216080:0.176915:0.216080:0.160246:0.073070:0.160246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Sean { , , , }, {1, 2, 3, 4} y la función de en definida como :@0.073089:0.200342:0.710499:0.200342:0.710499:0.184630:0.073089:0.184630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.146685:0.200342:0.156570:0.200342:0.156570:0.184907:0.146685:0.184907:0.000000 5:@0.163233:0.199788:0.178566:0.199788:0.178566:0.186072:0.163233:0.186072:0.000000 a b c d B:@0.190531:0.200342:0.280782:0.200342:0.280782:0.184907:0.190531:0.184907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.287445:0.199788:0.302778:0.199788:0.302778:0.186072:0.287445:0.186072:0.000000 f:@0.414510:0.200342:0.419204:0.200342:0.419204:0.184907:0.414510:0.184907:0.000000 A:@0.535998:0.200342:0.545883:0.200342:0.545883:0.184907:0.535998:0.184907:0.000000 B:@0.578372:0.200342:0.587207:0.200342:0.587207:0.184907:0.578372:0.184907:0.000000 :@0.706413:0.200342:0.710444:0.200342:0.710444:0.184630:0.706413:0.184630:0.000000 f a:@0.103281:0.216984:0.121964:0.216984:0.121964:0.201549:0.103281:0.201549:0.000000:0.000000:0.000000 ( ) 3, ( ) 2, ( ) 1, ( ) 4. :@0.107901:0.216984:0.387470:0.216984:0.387470:0.201272:0.107901:0.201272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.130634:0.216430:0.145967:0.216430:0.145967:0.202714:0.130634:0.202714:0.000000 f b:@0.177646:0.216984:0.196329:0.216984:0.196329:0.201549:0.177646:0.201549:0.000000:0.000000:0.000000 5:@0.204999:0.216430:0.220332:0.216430:0.220332:0.202714:0.204999:0.202714:0.000000 f c:@0.252011:0.216984:0.269093:0.216984:0.269093:0.201549:0.252011:0.201549:0.000000:0.000000:0.000000 5:@0.277763:0.216430:0.293096:0.216430:0.293096:0.202714:0.277763:0.202714:0.000000 f d:@0.324775:0.216984:0.343458:0.216984:0.343458:0.201549:0.324775:0.201549:0.000000:0.000000:0.000000 5:@0.352128:0.216430:0.367461:0.216430:0.367461:0.202714:0.352128:0.202714:0.000000 :@0.073089:0.240417:0.077120:0.240417:0.077120:0.224704:0.073089:0.224704:0.000000 Se tiene :@0.103203:0.240417:0.165486:0.240417:0.165486:0.224704:0.103203:0.224704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Rec f:@0.165362:0.240417:0.199047:0.240417:0.199047:0.224981:0.165362:0.224981:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) {1, 2, 3, 4} es decir, es función sobreyectiva.:@0.189549:0.240417:0.608634:0.240417:0.608634:0.224704:0.189549:0.224704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 5:@0.207717:0.239862:0.254968:0.239862:0.254968:0.226146:0.207717:0.226146:0.000000:0.000000:0.000000 B:@0.226915:0.240417:0.235751:0.240417:0.235751:0.224981:0.226915:0.224981:0.000000 5:@0.329205:0.239862:0.344538:0.239862:0.344538:0.226146:0.329205:0.226146:0.000000 B,:@0.348403:0.240417:0.360221:0.240417:0.360221:0.224981:0.348403:0.224981:0.000000:0.000000 f:@0.425971:0.240417:0.430665:0.240417:0.430665:0.224981:0.425971:0.224981:0.000000 2. Consideremos los conjuntos { 1, 0, 1, 2}, {5, 10, 15, 20} y la función de :@0.073089:0.263847:0.710389:0.263847:0.710389:0.248135:0.073089:0.248135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.318443:0.263847:0.328328:0.263847:0.328328:0.248412:0.318443:0.248412:0.000000 5 2:@0.333095:0.263293:0.373481:0.263293:0.373481:0.249577:0.333095:0.249577:0.000000:0.000000:0.000000 B:@0.446539:0.263847:0.455375:0.263847:0.455375:0.248412:0.446539:0.248412:0.000000 5:@0.460142:0.263293:0.475475:0.263293:0.475475:0.249577:0.460142:0.249577:0.000000 g:@0.594938:0.263847:0.604197:0.263847:0.604197:0.248412:0.594938:0.248412:0.000000 :@0.706321:0.263847:0.710352:0.263847:0.710352:0.248135:0.706321:0.248135:0.000000 A:@0.103189:0.280489:0.113073:0.280489:0.113073:0.265054:0.103189:0.265054:0.000000 en definida como:@0.113000:0.280489:0.257957:0.280489:0.257957:0.264777:0.113000:0.264777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.139524:0.280489:0.148360:0.280489:0.148360:0.265054:0.139524:0.265054:0.000000 :@0.073089:0.303921:0.077120:0.303921:0.077120:0.288209:0.073089:0.288209:0.000000 g:@0.103210:0.303921:0.112469:0.303921:0.112469:0.288486:0.103210:0.288486:0.000000 ( 1) 20, (0) 10, (1) 20, (2) 10.:@0.112395:0.303921:0.441075:0.303921:0.441075:0.288209:0.112395:0.288209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.117199:0.303367:0.165426:0.303367:0.165426:0.289651:0.117199:0.289651:0.000000:0.000000:0.000000 g:@0.202057:0.303921:0.211316:0.303921:0.211316:0.288486:0.202057:0.288486:0.000000 5:@0.233680:0.303367:0.249014:0.303367:0.249014:0.289651:0.233680:0.289651:0.000000 g:@0.285644:0.303921:0.294903:0.303921:0.294903:0.288486:0.285644:0.288486:0.000000 5:@0.317268:0.303367:0.332601:0.303367:0.332601:0.289651:0.317268:0.289651:0.000000 g:@0.369231:0.303921:0.378490:0.303921:0.378490:0.288486:0.369231:0.288486:0.000000 5:@0.400855:0.303367:0.416188:0.303367:0.416188:0.289651:0.400855:0.289651:0.000000 Entonces,:@0.103203:0.327354:0.173212:0.327354:0.173212:0.311641:0.103203:0.311641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Rec g:@0.177117:0.327354:0.215367:0.327354:0.215367:0.311918:0.177117:0.311918:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) {10, 20} por lo que no es sobreyectiva. :@0.201304:0.327354:0.568419:0.327354:0.568419:0.311641:0.201304:0.311641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.224037:0.326799:0.239370:0.326799:0.239370:0.313083:0.224037:0.313083:0.000000 ±:@0.299452:0.327895:0.314785:0.327895:0.314785:0.312723:0.299452:0.312723:0.000000 B,:@0.318650:0.327354:0.330468:0.327354:0.330468:0.311918:0.318650:0.311918:0.000000:0.000000 g:@0.413319:0.327354:0.422578:0.327354:0.422578:0.311918:0.413319:0.311918:0.000000 3.3 Función biyectiva:@0.073079:0.350791:0.239232:0.350791:0.239232:0.333844:0.073079:0.333844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.073079:0.374228:0.151047:0.374228:0.151047:0.357559:0.073079:0.357559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . :@0.150942:0.374228:0.159023:0.374228:0.159023:0.357281:0.150942:0.357281:0.000000:0.000000 Sean y dos conjuntos no vacíos cualesquiera. Una función o aplicación :@0.159115:0.374228:0.710357:0.374228:0.710357:0.358516:0.159115:0.358516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A B:@0.198690:0.374228:0.233609:0.374228:0.233609:0.358793:0.198690:0.358793:0.000000:0.000000:0.000000 f:@0.701632:0.374228:0.706326:0.374228:0.706326:0.358793:0.701632:0.358793:0.000000 de en es biyectiva si y solo si es inyectiva y sobreyectiva. :@0.073079:0.390870:0.515538:0.390870:0.515538:0.375157:0.073079:0.375157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.095812:0.390870:0.105697:0.390870:0.105697:0.375435:0.095812:0.375435:0.000000 B:@0.132148:0.390870:0.140984:0.390870:0.140984:0.375435:0.132148:0.375435:0.000000 f:@0.308158:0.390870:0.312852:0.390870:0.312852:0.375435:0.308158:0.375435:0.000000 La negación de la biyectividad de una función se expresa como sigue: una función de :@0.073061:0.414307:0.710338:0.414307:0.710338:0.398595:0.073061:0.398595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.678549:0.414307:0.683243:0.414307:0.683243:0.398872:0.678549:0.398872:0.000000 A:@0.073061:0.430949:0.082946:0.430949:0.082946:0.415514:0.073061:0.415514:0.000000 en no es biyectiva si y solo si no es inyectiva o no es sobreyectiva.:@0.082872:0.430949:0.588887:0.430949:0.588887:0.415236:0.082872:0.415236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 B:@0.109397:0.430949:0.118232:0.430949:0.118232:0.415514:0.109397:0.415514:0.000000 f:@0.308839:0.430949:0.313533:0.430949:0.313533:0.415514:0.308839:0.415514:0.000000 f:@0.442384:0.430949:0.447078:0.430949:0.447078:0.415514:0.442384:0.415514:0.000000 Ejercicios resueltos:@0.073024:0.454386:0.216034:0.454386:0.216034:0.437717:0.073024:0.437717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Sea { 1, 0, 1, 2}, {5, 10, 15, 20}.:@0.073089:0.477797:0.382879:0.477797:0.382879:0.462084:0.073089:0.462084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.132835:0.477797:0.142720:0.477797:0.142720:0.462362:0.132835:0.462362:0.000000 5 2:@0.146604:0.477242:0.185922:0.477242:0.185922:0.463527:0.146604:0.463527:0.000000:0.000000:0.000000 B:@0.254525:0.477797:0.263361:0.477797:0.263361:0.462362:0.254525:0.462362:0.000000 5:@0.267245:0.477242:0.282578:0.477242:0.282578:0.463527:0.267245:0.463527:0.000000 :@0.073089:0.501229:0.077120:0.501229:0.077120:0.485517:0.073089:0.485517:0.000000 Se define la función de en como sigue: :@0.103203:0.501229:0.426254:0.501229:0.426254:0.485517:0.103203:0.485517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.250042:0.501229:0.257773:0.501229:0.257773:0.485794:0.250042:0.485794:0.000000 A:@0.284371:0.501229:0.294256:0.501229:0.294256:0.485794:0.284371:0.485794:0.000000 B:@0.320707:0.501229:0.329543:0.501229:0.329543:0.485794:0.320707:0.485794:0.000000 v:@0.073056:0.524667:0.080787:0.524667:0.080787:0.509231:0.073056:0.509231:0.000000 ( 1) 5, (0) 10, (1) 15, (2) 20.:@0.080713:0.524667:0.399858:0.524667:0.399858:0.508954:0.080713:0.508954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.085518:0.524112:0.133745:0.524112:0.133745:0.510396:0.085518:0.510396:0.000000:0.000000:0.000000 v:@0.165423:0.524667:0.173155:0.524667:0.173155:0.509231:0.165423:0.509231:0.000000 5:@0.195519:0.524112:0.210853:0.524112:0.210853:0.510396:0.195519:0.510396:0.000000 v:@0.247483:0.524667:0.255214:0.524667:0.255214:0.509231:0.247483:0.509231:0.000000 5:@0.277579:0.524112:0.292912:0.524112:0.292912:0.510396:0.277579:0.510396:0.000000 v:@0.329543:0.524667:0.337274:0.524667:0.337274:0.509231:0.329543:0.509231:0.000000 5:@0.359638:0.524112:0.374972:0.524112:0.374972:0.510396:0.359638:0.510396:0.000000 :@0.073089:0.548094:0.077120:0.548094:0.077120:0.532381:0.073089:0.532381:0.000000 La función es inyectiva. Como :@0.103203:0.548094:0.336453:0.548094:0.336453:0.532381:0.103203:0.532381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 v:@0.183903:0.548094:0.191634:0.548094:0.191634:0.532658:0.183903:0.532658:0.000000 Rec v:@0.336628:0.548094:0.373350:0.548094:0.373350:0.532658:0.336628:0.532658:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) , la función es sobreyectiva. Luego, es :@0.360815:0.548094:0.710350:0.548094:0.710350:0.532381:0.360815:0.532381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.382388:0.547539:0.397721:0.547539:0.397721:0.533823:0.382388:0.533823:0.000000 B:@0.401955:0.548094:0.410790:0.548094:0.410790:0.532658:0.401955:0.532658:0.000000 v:@0.494507:0.548094:0.502238:0.548094:0.502238:0.532658:0.494507:0.532658:0.000000 v:@0.678616:0.548094:0.686347:0.548094:0.686347:0.532658:0.678616:0.532658:0.000000 una función biyectiva.:@0.103168:0.564736:0.262579:0.564736:0.262579:0.549023:0.103168:0.549023:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. Se define una función . Demuestra o refuta que es biyectiva.:@0.073089:0.588167:0.559466:0.588167:0.559466:0.572454:0.073089:0.572454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.265700:0.588167:0.275014:0.588167:0.275014:0.572731:0.265700:0.572731:0.000000 u:@0.458608:0.588167:0.467922:0.588167:0.467922:0.572731:0.458608:0.572731:0.000000 R:@0.331420:0.607518:0.344710:0.607518:0.344710:0.594620:0.331420:0.594620:0.000000 :@0.344710:0.607823:0.349312:0.607823:0.349312:0.594107:0.344710:0.594107:0.000000 →:@0.349312:0.609057:0.367480:0.609057:0.367480:0.593442:0.349312:0.593442:0.000000 :@0.367480:0.608378:0.371511:0.608378:0.371511:0.592665:0.367480:0.592665:0.000000 :@0.371511:0.608378:0.374824:0.608378:0.374824:0.592942:0.371511:0.592942:0.000000 R:@0.374824:0.607518:0.388114:0.607518:0.388114:0.594620:0.374824:0.594620:0.000000 x:@0.331420:0.625730:0.338875:0.625730:0.338875:0.610295:0.331420:0.610295:0.000000 :@0.338875:0.625730:0.342906:0.625730:0.342906:0.610018:0.338875:0.610018:0.000000 →:@0.342906:0.626410:0.361074:0.626410:0.361074:0.610794:0.342906:0.610794:0.000000 :@0.361074:0.625176:0.365676:0.625176:0.365676:0.611460:0.361074:0.611460:0.000000 u x :@0.365676:0.625730:0.395514:0.625730:0.395514:0.610295:0.365676:0.610295:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.374990:0.625730:0.392201:0.625730:0.392201:0.610018:0.374990:0.610018:0.000000:0.000000:0.000000 5 2 1 :@0.395514:0.625176:0.461486:0.625176:0.461486:0.611460:0.395514:0.611460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.430782:0.625730:0.441551:0.625730:0.441551:0.610295:0.430782:0.610295:0.000000:0.000000 1:@0.461481:0.625730:0.470463:0.625730:0.470463:0.610018:0.461481:0.610018:0.000000 5:@0.325946:0.627367:0.329991:0.627367:0.329991:0.593269:0.325946:0.593269:0.000000 u:@0.311604:0.619009:0.320918:0.619009:0.320918:0.603574:0.311604:0.603574:0.000000 ::@0.320916:0.619009:0.324119:0.619009:0.324119:0.603297:0.320916:0.603297:0.000000 a. :@0.104633:0.654474:0.120077:0.654474:0.120077:0.638762:0.104633:0.638762:0.000000:0.000000:0.000000 Inyectividad:@0.134834:0.654474:0.218613:0.654474:0.218613:0.639039:0.134834:0.639039:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.677548:0.077120:0.677548:0.077120:0.661836:0.073089:0.661836:0.000000 ;:@0.133331:0.676994:0.145608:0.676994:0.145608:0.663278:0.133331:0.663278:0.000000 x x:@0.145516:0.677548:0.172619:0.677548:0.172619:0.662113:0.145516:0.662113:0.000000:0.000000:0.000000 1:@0.152905:0.680721:0.158142:0.680721:0.158142:0.671560:0.152905:0.671560:0.000000 , ; ( ) ( ).:@0.158096:0.677548:0.382596:0.677548:0.382596:0.661836:0.158096:0.661836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.172557:0.680721:0.177794:0.680721:0.177794:0.671560:0.172557:0.671560:0.000000 [:@0.181697:0.677258:0.196333:0.677258:0.196333:0.663848:0.181697:0.663848:0.000000 R:@0.200203:0.676688:0.213493:0.676688:0.213493:0.663791:0.200203:0.663791:0.000000 x:@0.228366:0.677548:0.235821:0.677548:0.235821:0.662113:0.228366:0.662113:0.000000 1:@0.235756:0.680721:0.240993:0.680721:0.240993:0.671560:0.235756:0.671560:0.000000 ±:@0.244904:0.678089:0.260238:0.678089:0.260238:0.662917:0.244904:0.662917:0.000000 x:@0.264103:0.677548:0.271558:0.677548:0.271558:0.662113:0.264103:0.662113:0.000000 2:@0.271478:0.680721:0.276715:0.680721:0.276715:0.671560:0.271478:0.671560:0.000000 ⇒:@0.280624:0.677132:0.298792:0.677132:0.298792:0.660144:0.280624:0.660144:0.000000 f x:@0.302658:0.677548:0.319537:0.677548:0.319537:0.662113:0.302658:0.662113:0.000000:0.000000:0.000000 1:@0.319455:0.680721:0.324692:0.680721:0.324692:0.671560:0.319455:0.671560:0.000000 ±:@0.333388:0.678089:0.348721:0.678089:0.348721:0.662917:0.333388:0.662917:0.000000 f x:@0.352587:0.677548:0.369466:0.677548:0.369466:0.662113:0.352587:0.662113:0.000000:0.000000:0.000000 2:@0.369398:0.680721:0.374634:0.680721:0.374634:0.671560:0.369398:0.671560:0.000000 Supongamos ( ) f( ), entonces se tiene que::@0.133336:0.700624:0.482168:0.700624:0.482168:0.684911:0.133336:0.684911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.234713:0.700624:0.251593:0.700624:0.251593:0.685188:0.234713:0.685188:0.000000:0.000000:0.000000 1:@0.251526:0.703796:0.256763:0.703796:0.256763:0.694636:0.251526:0.694636:0.000000 5:@0.265460:0.700069:0.280793:0.700069:0.280793:0.686353:0.265460:0.686353:0.000000 x:@0.294194:0.700624:0.301649:0.700624:0.301649:0.685188:0.294194:0.685188:0.000000 2:@0.301584:0.703796:0.306820:0.703796:0.306820:0.694636:0.301584:0.694636:0.000000 :@0.073089:0.723698:0.077120:0.723698:0.077120:0.707985:0.073089:0.707985:0.000000 2:@0.133331:0.723143:0.148664:0.723143:0.148664:0.709428:0.133331:0.709428:0.000000 ( ) 1 ( ) 1. Por la ley cancelativa: .:@0.148572:0.723698:0.511179:0.723698:0.511179:0.707985:0.148572:0.707985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.153376:0.723698:0.160831:0.723698:0.160831:0.708263:0.153376:0.708263:0.000000 1:@0.160758:0.726870:0.165995:0.726870:0.165995:0.717710:0.160758:0.717710:0.000000 1 5 2:@0.174691:0.723143:0.241270:0.723143:0.241270:0.709428:0.174691:0.709428:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.245982:0.723698:0.253437:0.723698:0.253437:0.708263:0.245982:0.708263:0.000000 2:@0.253358:0.726870:0.258595:0.726870:0.258595:0.717710:0.253358:0.717710:0.000000 1:@0.267291:0.723143:0.282624:0.723143:0.282624:0.709428:0.267291:0.709428:0.000000 x:@0.459131:0.723698:0.466586:0.723698:0.466586:0.708263:0.459131:0.708263:0.000000 1:@0.466528:0.726870:0.471765:0.726870:0.471765:0.717710:0.466528:0.717710:0.000000 5:@0.475676:0.723143:0.491009:0.723143:0.491009:0.709428:0.475676:0.709428:0.000000 x:@0.494875:0.723698:0.502330:0.723698:0.502330:0.708263:0.494875:0.708263:0.000000 2:@0.502248:0.726870:0.507485:0.726870:0.507485:0.717710:0.502248:0.717710:0.000000 :@0.073089:0.746772:0.077120:0.746772:0.077120:0.731059:0.073089:0.731059:0.000000 Se comprueba que ( ) f( ) . Por lo tanto, la función es inyectiva.:@0.133336:0.746772:0.701175:0.746772:0.701175:0.731059:0.133336:0.731059:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.276182:0.746772:0.293061:0.746772:0.293061:0.731337:0.276182:0.731337:0.000000:0.000000:0.000000 1:@0.292994:0.749944:0.298231:0.749944:0.298231:0.740784:0.292994:0.740784:0.000000 5:@0.306928:0.746217:0.322262:0.746217:0.322262:0.732502:0.306928:0.732502:0.000000 x:@0.335662:0.746772:0.343117:0.746772:0.343117:0.731337:0.335662:0.731337:0.000000 2:@0.343052:0.749944:0.348289:0.749944:0.348289:0.740784:0.343052:0.740784:0.000000 ⇒:@0.356986:0.746356:0.375154:0.746356:0.375154:0.729367:0.356986:0.729367:0.000000 x:@0.379020:0.746772:0.386475:0.746772:0.386475:0.731337:0.379020:0.731337:0.000000 1:@0.386403:0.749944:0.391639:0.749944:0.391639:0.740784:0.386403:0.740784:0.000000 5:@0.395549:0.746217:0.410883:0.746217:0.410883:0.732502:0.395549:0.732502:0.000000 x:@0.414748:0.746772:0.422203:0.746772:0.422203:0.731337:0.414748:0.731337:0.000000 2:@0.422123:0.749944:0.427360:0.749944:0.427360:0.740784:0.422123:0.740784:0.000000 u:@0.600802:0.746772:0.610116:0.746772:0.610116:0.731337:0.600802:0.731337:0.000000 b. :@0.104633:0.769847:0.121531:0.769847:0.121531:0.754135:0.104633:0.754135:0.000000:0.000000:0.000000 Sobreyectividad:@0.134834:0.769847:0.244884:0.769847:0.244884:0.754412:0.134834:0.754412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.792922:0.077120:0.792922:0.077120:0.777209:0.073089:0.777209:0.000000 Rec u:@0.133331:0.792922:0.171636:0.792922:0.171636:0.777486:0.133331:0.777486:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) .:@0.157518:0.792922:0.215906:0.792922:0.215906:0.777209:0.157518:0.777209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.180306:0.792367:0.195639:0.792367:0.195639:0.778651:0.180306:0.778651:0.000000 R:@0.199505:0.792062:0.212795:0.792062:0.212795:0.779164:0.199505:0.779164:0.000000 Sean:@0.133336:0.815997:0.168818:0.815997:0.168818:0.800284:0.133336:0.800284:0.000000:0.000000:0.000000:0.000000 z :@0.172741:0.815997:0.183215:0.815997:0.183215:0.800562:0.172741:0.800562:0.000000:0.000000 [:@0.183156:0.815707:0.197793:0.815707:0.197793:0.802297:0.183156:0.802297:0.000000 , entonces :@0.197705:0.815997:0.293417:0.815997:0.293417:0.800284:0.197705:0.800284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.201662:0.815137:0.214952:0.815137:0.214952:0.802240:0.201662:0.802240:0.000000 z :@0.293275:0.815997:0.303749:0.815997:0.303749:0.800562:0.293275:0.800562:0.000000:0.000000 [:@0.303677:0.815707:0.318313:0.815707:0.318313:0.802297:0.303677:0.802297:0.000000 :@0.318225:0.815997:0.322257:0.815997:0.322257:0.800284:0.318225:0.800284:0.000000 Rec u:@0.322183:0.815997:0.360488:0.815997:0.360488:0.800562:0.322183:0.800562:0.000000:0.000000:0.000000:0.000000:0.000000 ( ), luego ( ), o sea:@0.346370:0.815997:0.519564:0.815997:0.519564:0.800284:0.346370:0.800284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.418250:0.815997:0.425485:0.815997:0.425485:0.800562:0.418250:0.800562:0.000000 5:@0.429368:0.815442:0.444702:0.815442:0.444702:0.801727:0.429368:0.801727:0.000000 u x:@0.448567:0.815997:0.470067:0.815997:0.470067:0.800562:0.448567:0.800562:0.000000:0.000000:0.000000 :@0.073089:0.839071:0.077120:0.839071:0.077120:0.823359:0.073089:0.823359:0.000000 z:@0.133331:0.839071:0.140565:0.839071:0.140565:0.823636:0.133331:0.823636:0.000000 :@0.140491:0.839071:0.163721:0.839071:0.163721:0.823359:0.140491:0.823359:0.000000:0.000000:0.000000 5 2 1:@0.144449:0.838516:0.205561:0.838516:0.205561:0.824801:0.144449:0.824801:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.178889:0.839071:0.186344:0.839071:0.186344:0.823636:0.178889:0.823636:0.000000 1, 1 .:@0.186270:0.839071:0.302291:0.839071:0.302291:0.823359:0.186270:0.823359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.229343:0.839071:0.236798:0.839071:0.236798:0.823636:0.229343:0.823636:0.000000 5 2:@0.240682:0.838516:0.288062:0.838516:0.288062:0.824801:0.240682:0.824801:0.000000:0.000000:0.000000 z:@0.291928:0.839071:0.299162:0.839071:0.299162:0.823636:0.291928:0.823636:0.000000 Resulta ( ) (1 ) 1 ,:@0.133336:0.862145:0.368591:0.862145:0.368591:0.846433:0.133336:0.846433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u x:@0.189617:0.862145:0.211117:0.862145:0.211117:0.846710:0.189617:0.846710:0.000000:0.000000:0.000000 5 2 2:@0.219787:0.861591:0.287213:0.861591:0.287213:0.847875:0.219787:0.847875:0.000000:0.000000:0.000000:0.000000:0.000000 z:@0.291078:0.862145:0.298312:0.862145:0.298312:0.846710:0.291078:0.846710:0.000000 1 5:@0.306982:0.861591:0.354362:0.861591:0.354362:0.847875:0.306982:0.847875:0.000000:0.000000:0.000000 z:@0.358228:0.862145:0.365462:0.862145:0.365462:0.846710:0.358228:0.846710:0.000000 :@0.073089:0.885221:0.077120:0.885221:0.077120:0.869508:0.073089:0.869508:0.000000 se concluye que es sobreyectiva.:@0.133336:0.885221:0.382921:0.885221:0.382921:0.869508:0.133336:0.869508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 u:@0.255258:0.885221:0.264572:0.885221:0.264572:0.869785:0.255258:0.869785:0.000000 :@0.073089:0.916233:0.077120:0.916233:0.077120:0.900521:0.073089:0.900521:0.000000 Por los literales a y b se ha demostrado que la función ::@0.133336:0.916233:0.537688:0.915706:0.537688:0.899993:0.133336:0.900521:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.544989:0.904213:0.558279:0.904213:0.558279:0.891316:0.544989:0.891316:0.000000 :@0.558279:0.904518:0.562881:0.904518:0.562881:0.890803:0.558279:0.890803:0.000000 →:@0.562881:0.905753:0.581049:0.905753:0.581049:0.890137:0.562881:0.890137:0.000000 :@0.581049:0.905073:0.585080:0.905073:0.585080:0.889361:0.581049:0.889361:0.000000 :@0.585080:0.905073:0.588394:0.905073:0.588394:0.889638:0.585080:0.889638:0.000000 R:@0.588394:0.904213:0.601684:0.904213:0.601684:0.891316:0.588394:0.891316:0.000000 x:@0.544989:0.922427:0.552444:0.922427:0.552444:0.906992:0.544989:0.906992:0.000000 :@0.552444:0.922427:0.556476:0.922427:0.556476:0.906714:0.552444:0.906714:0.000000 →:@0.556476:0.923106:0.574644:0.923106:0.574644:0.907491:0.556476:0.907491:0.000000 :@0.574644:0.921872:0.579245:0.921872:0.579245:0.908156:0.574644:0.908156:0.000000 u x :@0.579245:0.922427:0.609083:0.922427:0.609083:0.906992:0.579245:0.906992:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.588559:0.922427:0.605770:0.922427:0.605770:0.906714:0.588559:0.906714:0.000000:0.000000:0.000000 5 2 1 :@0.609083:0.921872:0.675055:0.921872:0.675055:0.908156:0.609083:0.908156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.644352:0.922427:0.655120:0.922427:0.655120:0.906992:0.644352:0.906992:0.000000:0.000000 1:@0.675050:0.922427:0.684033:0.922427:0.684033:0.906714:0.675050:0.906714:0.000000 5:@0.539516:0.924063:0.543561:0.924063:0.543561:0.889965:0.539516:0.889965:0.000000 u:@0.525172:0.915706:0.534486:0.915706:0.534486:0.900271:0.525172:0.900271:0.000000 :@0.073089:0.939308:0.077120:0.939308:0.077120:0.923595:0.073089:0.923595:0.000000 es inyectiva y sobreyectiva, por lo tanto, es biyectiva.:@0.133336:0.939308:0.511942:0.939308:0.511942:0.923595:0.133336:0.923595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En forma general, las :@0.744288:0.202047:0.884247:0.202047:0.884247:0.187763:0.744288:0.187763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 funciones (sean estas :@0.744288:0.217176:0.888099:0.217176:0.888099:0.202892:0.744288:0.202892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inyectivas, sobreyectivas :@0.744288:0.232305:0.908456:0.232305:0.908456:0.218021:0.744288:0.218021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o biyectivas) son muy :@0.744288:0.247434:0.890815:0.247434:0.890815:0.233150:0.744288:0.233150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 utilizadas para resolver :@0.744288:0.262563:0.897040:0.262563:0.897040:0.248279:0.744288:0.248279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 problemas de la vida :@0.744288:0.277692:0.885130:0.277692:0.885130:0.263407:0.744288:0.263407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 real. Por ejemplo, en la :@0.744288:0.292821:0.895638:0.292821:0.895638:0.278536:0.744288:0.278536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 geología, con el fin de :@0.744288:0.307950:0.893748:0.307950:0.893748:0.293665:0.744288:0.293665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 determinar la intensidad :@0.744288:0.323079:0.909197:0.323079:0.909197:0.308794:0.744288:0.308794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de un sismo, se utiliza :@0.744288:0.338207:0.890703:0.338207:0.890703:0.323923:0.744288:0.323923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una función denominada :@0.744288:0.353336:0.915961:0.353336:0.915961:0.339052:0.744288:0.339052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 escala de Richter.:@0.744288:0.368465:0.857089:0.368465:0.857089:0.354181:0.744288:0.354181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Investiga escribe:@0.744288:0.532418:0.870587:0.532418:0.870587:0.517264:0.744288:0.517264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.806652:0.532418:0.821210:0.532418:0.821210:0.518133:0.806652:0.518133:0.000000:0.000000:0.000000 otros :@0.870492:0.532418:0.911451:0.532418:0.911451:0.518133:0.870492:0.518133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ejemplos de aplicaciones :@0.744285:0.547547:0.914535:0.547547:0.914535:0.533262:0.744285:0.533262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de estas funciones.:@0.744285:0.562676:0.869146:0.562676:0.869146:0.548391:0.744285:0.548391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinaria :@0.740720:0.143074:0.864129:0.143074:0.864129:0.127668:0.740720:0.127668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática :@0.740720:0.158203:0.826214:0.158203:0.826214:0.143919:0.740720:0.143919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y geología:@0.740720:0.173332:0.809774:0.173332:0.809774:0.159048:0.740720:0.159048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000