Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 57

$ f^{-1}(x)=\frac{4}{x}$ See graph.

Step 1. $f(x)=\frac{4}{x}\Longrightarrow y=\frac{4}{x} \Longrightarrow x=\frac{4}{y}, \Longrightarrow y=\frac{4}{x}\Longrightarrow f^{-1}(x)=\frac{4}{x}$ Step 2. Check $f( f^{-1}(x))=\frac{4}{\frac{4}{x}}=x$ and $f^{-1}(f(x))=\frac{4}{\frac{4}{x}} =x$ Step 3. See graph for both $f$ and $f^{-1}$.