Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 292: 56

$ f^{-1}(x)=\sqrt {x-9}$ See graph.

Step 1. $f(x)=x^2+9, x\ge0\Longrightarrow y=x^2+9 \Longrightarrow x=y^2+9, y\ge0 \Longrightarrow y=\sqrt {x-9}\Longrightarrow f^{-1}(x)=\sqrt {x-9}$ Step 2. Check $f( f^{-1}(x))=(\sqrt {x-9})^2+9=x$ and $f^{-1}(f(x))=\sqrt {(x^2+9)-9} =x$ Step 3. See graph for both $f$ and $f^{-1}$.