Algebra and Trigonometry 10th Edition

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

Chapter 2 - Review Exercises - Page 234: 71


$\sqrt {\dfrac{x}{2}} +4$ Domain of the function $f$ is: $ x \geq 4$. Domain of the inverse of function $f$ is: $ x \geq 0$.

Work Step by Step

We have $y=2(x-4)^2$ To compute the inverse, we will have to interchange $x$ and $y$. or, $x=2(y-4)^2 \implies \dfrac{x}{2} =(y-4)^2$ or, $y-4=\sqrt {\dfrac{x}{2}} \implies y=\sqrt {\dfrac{x}{2}} +4$ Replace $y$ with $f^{-1} (x)$. so, $f^{-1} (x)=\sqrt {\dfrac{x}{2}} +4$
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