Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 72

$f^{-1}(x)=\frac{2x-4}{x+3}$

$f(x)=\frac{-3x-4}{x-2},$ $y=\frac{-3x-4}{x-2},$ a. $x=\frac{-3y-4}{y-2},$ $x(y-2)=-3y-4,$ $xy-2x=-3y-4,$ $xy+3y=2x-4,$ $y(x+3)=2x-4,$ $y=\frac{2x-4}{x+3}=f^{-1}(x),$ b. Domain of $f(x)$ is $x\in\mathbb{R} \ne 2$ and Domain of $f^{-1}(x)$ is $x\in\mathbb{R}\ne -3$