Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Review Exercises - Page 304: 116

Answer

The inverse function for $f\left( x \right)=1-{{x}^{2}},x\ge 0$ is ${{f}^{-1}}\left( x \right)=\sqrt{1-x}$ .

Work Step by Step

Consider the provided function: $f\left( x \right)=1-{{x}^{2}},x\ge 0$ Let $y=1-{{x}^{2}}$ The steps to find the inverse function $y=f\left( x \right)$ are as follows: Step 1: Interchange $x$ and $y$. $x=1-{{y}^{2}}$ Step 2: Solve the equation for $y$ . $\begin{align} & x=1-{{y}^{2}} \\ & {{y}^{2}}=1-x \\ & y=\sqrt{1-x} \end{align}$ Step 3: Replace $y$ with ${{f}^{-1}}\left( x \right)$ . ${{f}^{-1}}\left( x \right)=\sqrt{1-x}$ Therefore, the inverse function for $f\left( x \right)=1-{{x}^{2}},x\ge 0$ is ${{f}^{-1}}\left( x \right)=\sqrt{1-x}$.
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