Answer
$f^{-1}(x)=\frac{-2x}{x-3}$
Work Step by Step
$f(x)=\frac{3x}{x+2},$
$y=\frac{3x}{x+2},$
a.
$x=\frac{3y}{y+2},$
$x(y+2)=3y,$
$xy+2x-3y=0,$
$y(x-3)=-2x,$
$y=\frac{-2x}{x-3}=f^{-1}(x)$
b. Domain of $f(x)$ is, $x \in \mathbb{R} \ne -2$ and Domain of $f^{-1}(x)$ is, $x \in \mathbb{R} \ne 3$
