Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 67

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

Step 1. $f(x)=\frac{3x+4}{2x-3} \Longrightarrow y=\frac{3x+4}{2x-3} \Longrightarrow x=\frac{3y+4}{2y-3} \Longrightarrow y=\frac{3x+4}{2x-3} \Longrightarrow f^{-1}(x)=\frac{3x+4}{2x-3}$ Step 2. Check $f(f^{-1}(x))=\frac{3(\frac{3x+4}{2x-3})+4}{2(\frac{3x+4}{2x-3})-3}=x$ and $f^{-1}(f(x))=\frac{3(\frac{3x+4}{2x-3})+4}{2(\frac{3x+4}{2x-3})-3}=x$