What is the inverse function for f(x) = x/(x-2)?

1 Answer
Sep 22, 2015

f^(-1)(x) = (2 x) / (x - 1)

Explanation:

Setting y = f(x)

y = x/(x-2)

this may be rearranged (intermediate steps shown) as follows

y(x-2) = x

x*y - 2 y = x

x*y - x = 2 y

x(y - 1) = 2 y

x = (2y) / (y - 1)

This expression shows x in terms of y.

That is, it is the inverse of function f(x).

That is,

f^(-1)(x) = (2 x) / (x - 1)

as required.