Answer
$f^{-1}(x)=\sqrt[3]x -2$
Work Step by Step
$f(x)=(x+2)^3$
$y=(x+2)^3$
a.
$x=(y+2)^3$
$\sqrt[3]x -2=y$
$f^{-1}(x)=\sqrt[3]x -2$
b.
$f(f^{-1}(x)))=(\sqrt[3]x -2+2)^3=(\sqrt[3] x)^3=x$
and
$f^{-1}(f(x))=\sqrt[3] {(x+2)^3}=x+2-2=x$
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: 33
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