Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.1 - Inverse Functions and Their Derivatives - Exercises 7.1 - Page 372: 20

Answer

$$ f^{-1}(x)=-\sqrt x $$

Work Step by Step

Given $$ y=x^{2}$$ Solve for $x$: \begin{aligned} & y=x^{2}\\ & \Rightarrow x^{2}=y \\ &\Rightarrow x=-\sqrt{y}, \ \ \ \text{Since}, x\leq 0 \\ \text{Switch $ x $ and $ y $}\\ &y=-\sqrt{x}=f^{-1}(x) \end{aligned}
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