# Thread: find the inverse function

1. ## find the inverse function

find the inverse function
f(x)=4x/(x-2)

2. ## Re: find the inverse function

$f(x)=\frac{4x}{x-2}$
$x=\frac{4y}{y-2}$
$\Leftrightarrow x(y-2)=4y$
$\Leftrightarrow xy-2x=4y$
$\Leftrightarrow xy-4y=2x$
$\Leftrightarrow y(x-4)=2x$
$\Leftrightarrow y=\frac{2x}{x-4}$

Thus the inverse function:
$f^{-1}(x)=\frac{2x}{x-4}$