Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 53

$f^{-1}(x)=\sqrt[3] {x+1} $ See graph.

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