College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises: 98

Answer

$f^{-1}(x)=2+(x-1)^{5}$

Work Step by Step

We are given: $f(x)=1+\sqrt[5]{x-2}$ To find the inverse function, we switch $x$ and $y$ and solve for $y$: $y=1+\sqrt[5]{x-2}$ $x=1+\sqrt[5]{y-2}$ $x-1=\sqrt[5]{y-2}$ $(x-1)^5=y-2$ $(x-1)^5+2=y$ Thus the inverse is: $f^{-1}(x)=2+(x-1)^{5}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.