Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 421: 69

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

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