Question

If f(x)= x/x-1 for x =\= 1. Show that f(f(x))=x for x=\= 1.

Please help and give an explanation, I find this super confusing.

Answer 1

Answer:

$f(x) = \frac{x}{x - 1} \\ f(f(x)) = \frac{ \frac{x}{x - 1} }{ \frac{x}{x - 1} - 1} \\ f(f(x)) = \frac{x}{1 } \\ f(f(x)) = x \: \: \: (proved)$