Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 70

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

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