Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 71

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

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