Answer
$f^{-1}(x) = \sqrt[3] {\frac{x - 5}{-4}}$
Work Step by Step
$f(x) = 5 - 4x^{3}$
$y = 5 - 4x^{3}$
$y - 5 = -4x^{3}$
$\frac{y - 5}{-4} = x^{3}$
$\sqrt[3] {\frac{y - 5}{-4}} = x$
$f^{-1}(x) = \sqrt[3] {\frac{x - 5}{-4}}$
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: 51
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