Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 10 - Compositions, Inverses, and Combinations of Functions - 10.2 Invertibility and Properties of Inverse Functions - Exercises and Problems for Section 10.2 - Exercises and Problems - Page 411: 36

Answer

$$y=\sqrt{\sqrt{x}-1},\:y=-\sqrt{\sqrt{x}-1},\:y=\sqrt{-\sqrt{x}-1},\:y=-\sqrt{-\sqrt{x}-1}$$

Work Step by Step

Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is: $$x=\left(1+y^2\right)^2 \\ y=\sqrt{\sqrt{x}-1},\:y=-\sqrt{\sqrt{x}-1},\:y=\sqrt{-\sqrt{x}-1},\:y=-\sqrt{-\sqrt{x}-1}$$
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