Answer
$f^{-1}(x)=\sqrt[3]x +1$
Work Step by Step
$f(x)=(x-1)^3$
$y=(x-1)^3$
a.
$x=(y-1)^3$
$\sqrt[3]x +1=y$
$f^{-1}(x)=\sqrt[3]x +1$
b.
$f(f^{-1}(x)))=(\sqrt[3]x +1-1)^3=(\sqrt[3] x)^3=x$
and
$f^{-1}(f(x))=\sqrt[3] {(x-1)^3+1}=x-1+1=x$
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: 34
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