Answer
$f^{-1}(x) = 0.4^{x}$
Work Step by Step
$f(x) =\log_{0.4} x$
Let $f(x) = y$
$y = \log_{0.4} x$
Swap the $x$ and $y$ variable to find the inverse:
$x =\log_{0.4} y$
$y =0.4^{x}$
$f^{-1}(x) = 0.4^{x}$
Intermediate Algebra: Connecting Concepts through Application
by Clark, Mark; Anfinson, Cynthia
Published by
Brooks Cole
ISBN 10:
0-53449-636-9
ISBN 13:
978-0-53449-636-4
Chapter 6 - Logarithmic Functions - 6.3 Graphing Logarithmic Functions - 6.3 Exercises - Page 511: 44
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