Answer
$f^{-1}(x) = \frac{1}{\sqrt x}, x\gt0$
Work Step by Step
$f(x) = \frac{1}{x^{2}}, x\gt0$
$y = \frac{1}{x^{2}}$
$x^{2} = \frac{1}{y}$
$x = \sqrt {\frac{1}{y}}$
$x = \frac{1}{\sqrt y}$
$f^{-1}(x) = \frac{1}{\sqrt x}, x\gt0$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 263: 64
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