Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 227: 69

Answer

$f^{-1}(x)=(x-2)^{3}$

Work Step by Step

$f(x)=2+\sqrt[3]{x}$ Rewrite this expression as $y=2+\sqrt[3]{x}$ and solve for $x$: $y=2+\sqrt[3]{x}$ Take $2$ to the left side: $y-2=\sqrt[3]{x}$ $\sqrt[3]{x}=y-2$ Cube both sides: $(\sqrt[3]{x})^{3}=(y-2)^{3}$ $x=(y-2)^{3}$ Interchange $x$ and $y$: $y=(x-2)^{3}$ The inverse of the original function is $f^{-1}(x)=(x-2)^{3}$
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.