Question

The function f is defined as `f(x) = x/(x-1)`, how do you find `f(f(x))`?

Answer 1

Substitute f(x) for every x and then simplify.

Explanation:

Given: `f(x) = x/(x-1)`

Substitute f(x) for every x

`f(f(x)) = (x/(x-1))/((x/(x-1))-1)`

Multiply numerator and denominator by 1 in the form of `(x-1)/(x-1)`

`f(f(x)) = (x/(x-1))/((x/(x-1))-1)(x-1)/(x-1)`

`f(f(x)) = (x)/(x-x+1)`

`f(f(x)) = (x)/1`

`f(f(x)) = x`

This means that `f(x) = x/(x-1)` is its own inverse.