$y=\frac{3x}{x+2}$

$y(x+2)=3x$

$yx+2y=3x$

$yx-3x=-2y$

$x(y-3)=-2y$

$x=\frac{-2y}{y-3}$

$f^{-1}(x)=\frac{-2x}{x-3}$

Follow the steps in part (a).

What are the domain and range of the original function?
How does this affect the domain of the inverse function?