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: 76


$f^{-1} (x)=\sqrt {2x+2}$ Domain of the function $f$ is: $[0, \infty)$. Domain of the inverse of function $f$ is: $[-1,\infty)$.

Work Step by Step

We have $y=\dfrac{1}{2}x^2-1$ To compute the inverse, we will have to interchange $x$ and $y$. $y=\dfrac{1}{2}y^2-1$ Re-write as: $ y=\sqrt {2x+2}$ Replace $y$ with $f^{-1} (x)$. so, $f^{-1} (x)=\sqrt {2x+2}$
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