Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 52

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

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