Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 59

$f^{-1}(x)=\frac{1}{x}+2$ See graph.

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