Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 49

$ f^{-1}(x)=\frac{1}{3}x $ See graph.

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