# Given f(x)=1/(x-2), how do you find f(f^-1(x))?

Mar 9, 2016

First we must find the inverse.

#### Explanation:

The inverse can be found algebraically by switching y with x and vice versa.

$y = \frac{1}{x - 2}$

$x = \frac{1}{y - 2}$

$x \left(y - 2\right) = 1$

$y - 2 = \frac{1}{x}$

$y = \frac{1}{x} + 2$

We must now plug this into function ƒ, as the notation ƒ(ƒ^-1(x)) denotes.\

ƒ(x) = 1/(1/x + 2)

So, ƒ(ƒ^-1(x)) = 1/(1/x + 2)