Fun\303\247\303\265es Inversas: Exemplos de Fun\303\247\303\265es Inversas S A T O R A R E P O T E N E T O P E R A R O T A S 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 O Sator Square \303\251 um pal\303\255ndromo em latim dos tempos de Roma, com as palavras SATOR AREPO TENET OPERA ROTAS. Embora n\303\243o estar completamente clara, o significado da senten\303\247a \303\251 algo como: "O fazendeiro, Arepo (um nome pr\303\263prio), usa seu arado como sua forma de trabalho." Conex\303\265es m\303\255sticas tem sido sugeridas com o quadrado, a partir dos anagramas Crist\303\243os (as letras podem ser rearranjadas para formar uma cruz de "Pater Noster"' (Ora\303\247\303\243o do Senhor) com dois As e dois Os sobrando, tomadas para representar o Alfa e o \303\224mega) aos encantos da magia popular (uma cren\303\247a comum era que pal\303\255ndromos confundiam o dem\303\264nio). Pode ser lido em diversos modos: da esquerda para a direita, da direita para a esquerda, de cima para baixo, de baixo para cima, ou mesmo boustrophedon (da esquerda para a direita em uma linha, e da diretta para a esquerda na outra). Uma rearruma\303\247\303\243o pode inverter ou caso contr\303\241rio mudar a ordem das palavras, mas como a ordem das palavras em latim era relaxada, o significado continua o mesmo.

Nesta apresenta\303\247\303\243o, vamos olhar para exemplos de inversas de algumas das mais importantes fun\303\247\303\265es da matem\303\241tica. Assumiremos que voc\303\252 est\303\241 familiar com esses termos adicionais, que s\303\243o definidos em ordem de apresenta\303\247\303\265es dessa cole\303\247\303\243o: fun\303\247\303\243o, inversa, um-pra-um, dom\303\255nio, e alcance.

As inversas de algumas fun\303\247\303\265es importantes s\303\243o t\303\243o comumente usadas possuem nomes pr\303\263prios: Fun\303\247\303\243o Fun\303\247\303\243o Inversa Fun\303\247\303\243o Fun\303\247\303\243o Inversa Fun\303\247\303\243o Fun\303\247\303\243o Inversa LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkc2VuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjc2VuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkY3NjRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjY3NjRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkc2VjRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjc2VjRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkY290RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnYXJjY290RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEjbG5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0YxLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRInhGJy9GMFEldHJ1ZUYnRjIvRjVRJ2l0YWxpY0YnRjJGNEYyRjRGMkY0 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1JJW1zdXBHRiQ2JS1GOTYuUS8mRXhwb25lbnRpYWxFO0YnRjJGPEY+RkBGQkZERkZGSEZKRkwvRlBRLDAuMTExMTExMWVtRictRiM2JUYrRjJGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkY8 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

Existe claramente um problema com as "inversas" mostradas em , pois muitas das fun\303\247\303\265es listadas nessa t\303\241bua n\303\243o s\303\243o um-pra-um, e portanto n\303\243o s\303\243o invert\303\255veis. Por exemplo, 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, 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, e assim por diante. Para resolver essa situa\303\247\303\243o, \303\251 costume restringir o dom\303\255nio da fun\303\247\303\243o original a um subdom\303\255nio no qual a fun\303\247\303\243o \303\251 invert\303\255vel. Esse subdom\303\255nio poderia ser grande o suficiente para que todos os valores poss\303\255veis da fun\303\247\303\243o original sejam obtidos pela fun\303\247\303\243o restrita nesse subdom\303\255nio. Isto \303\251, que o alcance da fun\303\247\303\243o restrita a esse subdom\303\255nio deveria possuir o mesmo alcance da fun\303\247\303\243o original. Para a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEic0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiZRImVGJ0YvRjJGNC1GLDYmUSJuRidGL0YyRjQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA==, \303\251 normal restrig\303\255-la no intervalo 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. Esses gr\303\241ficos mostram a fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEic0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiZRImVGJ0YvRjJGNC1GLDYmUSJuRidGL0YyRjQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== nesse dom\303\255nio restrito e sua fun\303\247\303\243o inversa, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlElYXJjc0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiZRImVGJ0YvRjJGNC1GLDYmUSJuRidGL0YyRjQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA==: 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Note que o alcance da fun\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlElYXJjc0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiZRImVGJ0YvRjJGNC1GLDYmUSJuRidGL0YyRjQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA== \303\251 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, que \303\251 o dom\303\255nio da fun\303\247\303\243o (restrita) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEic0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYsNiZRImVGJ0YvRjJGNC1GLDYmUSJuRidGL0YyRjQtSShtZmVuY2VkR0YkNiUtRiM2JS1GLDYmUSJ4RicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJ0YyRjRGMkY0RjJGNA==. Alguns autores tamb\303\251m usam a nota\303\247\303\243o 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 para a fun\303\247\303\243o arcsen, e similarmente para as outras fun\303\247\303\265es trigonom\303\251tricas. Essa nota\303\247\303\243o est\303\241 mais de acordo com a nota\303\247\303\243o gen\303\251rica 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. \303\211 importante lembrar que 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, n\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYpLUkjbWlHRiQ2JlEic0YnLyUnaXRhbGljR0Y0RjJGNS1GOzYmUSJlRidGPkYyRjUtRjs2JlEibkYnRj5GMkY1LUkobWZlbmNlZEdGJDYlLUYjNiYtRjs2JlEieEYnL0Y/USV0cnVlRidGMi9GNlEnaXRhbGljRidGTkYyRlBGMkY1Rk5GMkZQLyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZWLyUpYmV2ZWxsZWRHRjRGMkY1.

O \303\272ltimo par de fun\303\247\303\265es mostrado em \303\251 um muito importante em uma grande variedade de aplica\303\247\303\265es matem\303\241ticas e cient\303\255ficas, mas somente foi nomeada recentemente. A inversa de 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 foi introduzida, com a nota\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA=, no sistema simb\303\263lico computacional do Maple nos anos 1980. Nos anos 1990, um grupo de pesquisadores decidiram estudar essa fun\303\247\303\243o detalhadamente, e descobriram que tinha uma hist\303\263ria rica e largamente desconhecida dado ao fato que a fun\303\247\303\243o inversa n\303\243o tinha nome. Como uma remedia\303\247\303\243o parcial dessa situa\303\247\303\243o, a fun\303\247\303\243o inversa LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiV0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEieEYnRi9GMkY1RjIvRjZRJ25vcm1hbEYnRjJGQEYyRkA= foi nomeada como fun\303\247\303\243o W de Lambert, ap\303\263s Johann Heinrich Lambert, um matem\303\241tico su\303\255\303\247o do s\303\251culo 18 que foi um dos pioneiros do estudo dessa fun\303\247\303\243o e suas propriedades.

Na demonstra\303\247\303\243o abaixo, escolha uma fun\303\247\303\243o na lista Selecione fun\303\247\303\243o. O gr\303\241fico da fun\303\247\303\243o \303\251 mostrado no primeiro gr\303\241fico. Clique em Mostrar Restri\303\247\303\243o Invers\303\255vel e a restri\303\247\303\243o padr\303\243o no gr\303\241fico ficar\303\241 em destaque no segundo gr\303\241fico. Finalmente, clique em Inverter Fun\303\247\303\243o Restrita para mostrar o resultado da invers\303\243o da fun\303\247\303\243o no \303\272ltimo gr\303\241fico. Tente selecionar fun\303\247\303\265es diferentes. Selecionar fun\303\247\303\243o: x,sin(x),cos(x),tan(x),arcsin(x),arccos(x),arctan(x),e^x,10^x,ln(x),1/x,x^2,x^3,x+sin(x),x*e^xM4_5_4a:-SelChange(); M4_5_4a:-Show(); M4_5_4a:-Invert(); 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 NiotJiUmX0FYSVNHNiMiIiI2Ji0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0mJSZfQVhJU0c2IyIiIzYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUrQVhFU0xBQkVMU0c2JFEieDYiUSJ5NiItJSpUSElDS05FU1NHNiMiIiMtJSVGT05URzYkJSZUSU1FU0ciIzctJSlfVklTSUJMRUc2IyIiIi0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJD8iISIiLSUpQk9VTkRTX1lHNiMkIiQ1JSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJXFEISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJStBISIiLSUpQ0hJTERSRU5HNiItJStBTk5PVEFUSU9ORzYnLSUpQk9VTkRTX1hHNiMkIiQhPSEiIi0lKUJPVU5EU19ZRzYjJCIkSSIhIiItJS1CT1VORFNfV0lEVEhHNiMkIiVnQiEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhUiMhIiItJSlDSElMRFJFTkc2Ig==Ig== 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Ig==

"Sator Arepo Tenet Opera Rotas" \303\251 um pal\303\255ndromo porque l\303\252-se igualmente da esquerda para a direita e da direita para a esquerda. Similarmente, um n\303\272mero como 12321 \303\251 um n\303\272mero pal\303\255ndromo porque l\303\252-se igualmente de tr\303\241s-para-a-frente. Um m\303\251todo de constru\303\247\303\243o de n\303\272meros pal\303\255ndromos de n\303\272meros n\303\243o-pal\303\255ndromos envolve adi\303\247\303\243o do reverso do n\303\272mero n\303\243o-pal\303\255ndromo por ele mesmo. Por exemplo, For example, 12 n\303\243o \303\251 um pal\303\255ndromo, mas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JVEjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi5RIitGJ0YvRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZJLUYsNiVRIzIxRidGL0YyLUY2Ni5RIj1GJ0YvRjJGOUY7Rj1GP0ZBRkNGRS9GSFEsMC4yNzc3Nzc4ZW1GJy9GS0ZTLUYsNiVRIzMzRidGL0YyRi9GMg==, que \303\251 um pal\303\255ndromo. Nem todos os n\303\272meros se tornam pal\303\255ndromos depois de um passo. Alguns requerem dois, tr\303\252s, ou mais passos para se tornar um pal\303\255ndromo. Um n\303\272mero que que nunca se torna um pal\303\255ndromo atrav\303\251s desse processo repetido \303\251 conhecido como um n\303\272mero de Lychrel (um nome inventado pelo criador desse m\303\251todo). Nenhum n\303\272mero j\303\241 foi provado ser n\303\272mero de Lychrel, apesar de existirem n\303\272meros que ap\303\263s muitos milh\303\265es de itera\303\247\303\265es n\303\243o se tornaram pal\303\255ndromos (o menor desses n\303\272meros \303\251 196). Entre com um n\303\272mero positivo (menor que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JVEjMTBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUYvNiVRIjhGJ0YyRjUvJSdpdGFsaWNHUSV0cnVlRidGMi9GNlEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjJGNQ==) na primeira caixa e pressione Apply Lychrel Process. O pal\303\255ndromo criado pela aplica\303\247\303\243o do processo de Lychrel ao seu n\303\272mero \303\251 mostrado ao junto com as itera\303\247\303\265es requeridas para obt\303\252-lo. 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M4_5_4b:-Eval();LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYrLUYsNi5RKCZzcmFycjtGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZDRkZGK0YrRi9GMg== O processo de Lychrel \303\251 uma fun\303\247\303\243o? \303\211 um-pra-um?

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 JSFH