Answer
$f^{-1}(x)=\sqrt[3] {x-2}$
Work Step by Step
$f(x)=x^3+2$
$y=x^3+2$
a.
$x=y^3+2$
$x-2=y^3$
$f^{-1}(x)=\sqrt[3] {x-2}$
b.
$f(f^{-1}(x)))=(\sqrt[3] {x-2})^2+2=x-2+2=x$
and
$f^{-1}(f(x))=\sqrt[3] {x^3+2-2}=\sqrt[3] {x^3}=x$
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 9 - Section 9.2 - Composite and Inverse Functions - Exercise Set - Page 687: 31
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