College Algebra 7th Edition

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: 51

Answer

$f^{-1}(x) = \sqrt[3] {\frac{x - 5}{-4}}$

Work Step by Step

$f(x) = 5 - 4x^{3}$ $y = 5 - 4x^{3}$ $y - 5 = -4x^{3}$ $\frac{y - 5}{-4} = x^{3}$ $\sqrt[3] {\frac{y - 5}{-4}} = x$ $f^{-1}(x) = \sqrt[3] {\frac{x - 5}{-4}}$
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