#### Answer

$g(x)=\frac{2x}{x-1}$

#### Work Step by Step

$f(x)=\frac{x}{x-2}$
$(f\circ g)(x)=x$
$g(x)=?$
Let's say $\ g(x)=y\ $, so that the composition of the two functions is represented as:
$(f\circ g)(x)=f(g(x))$
$f(y)=\frac{y}{y-2}$
$x=\frac{y}{y-2}$
$yx-2x=y$
$y(x-1)=2x$
$y=\frac{2x}{x-1}$
$g(x)=\frac{2x}{x-1}$