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: 75


$f^{-1} (x)=\sqrt {\dfrac{5-x}{2}}$ Domain of the function $f$ is: $[0, \infty)$. Domain of the inverse of function $f$ is: $(-\infty, 5]$.

Work Step by Step

We have $y=-2x^2+5$ To compute the inverse, we will have to interchange $x$ and $y$. $x=-2y^2+5$ Re-write as: $ y=\sqrt {\dfrac{5-x}{2}}$ Replace $y$ with $f^{-1} (x)$. so, $f^{-1} (x)=\sqrt {\dfrac{5-x}{2}}$
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