Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 229: 61


$f^{-1} (x) =-3+\sqrt x$

Work Step by Step

When we apply the horizontal test, it has been noticed that the function is one-to-one and verifies the horizontal test. Therefore, the function has an inverse function. To compute the inverse, we will have to interchange $y$ and $x$. $x=(y+3)^2 \implies y+3= \pm \sqrt x$ or, $y=-3 \pm \sqrt x$ Since the domain for the function is $x \geq -3$, we neglect $-3-\sqrt x$ So, we have $y=-3+\sqrt x$ Replace $y$ with $f^{-1} (x) =-3+\sqrt x$
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