Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 70

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

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