Answer
$f^{-1}(x)=\frac{1}{x}$
Work Step by Step
$f(x)=\frac{1}{x}$
$y=\frac{1}{x}$
a.
$x=\frac{1}{y}$
$y=\frac{1}{x}$
$f^{-1}(x)=\frac{1}{x}$
b.
$f(f^{-1}(x))=\frac{1}{\frac{1}{x}}=x$
and
$f^{-1}(f(x))=\frac{1}{\frac{1}{x}}=x$
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: 35
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