Question

dada a funçao f(x)=x/x-1 definida para todo real x 1.nessas condiçoes,calcule f(f(x))

Answer 1

É dada a função

$f(x)=\dfrac{x}{x-1}$

com $x\ne 1.$


Se $f(x)=\dfrac{x}{x-1}\,,$ então,

$f(f(x))=\dfrac{f(x)}{f(x)-1}\\\\\\ f(f(x))=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-1}\\\\\\ f(f(x))=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-\frac{x-1}{x-1}}\\\\\\ f(f(x))=\dfrac{\frac{x}{x-1}}{\left(\frac{x-(x-1)}{x-1}\right )}\\\\\\ f(f(x))=\dfrac{\frac{x}{x-1}}{\left(\frac{1}{x-1}\right )}\\\\\\ f(f(x))=\dfrac{x}{x-1}\cdot \dfrac{x-1}{1}\\\\\\ \boxed{\begin{array}{c} f(f(x))=x \end{array}}~~~~x\ne 1.$

Answer 2

Bons estudos!!!

Boa noite!!!!