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: 3

Answer

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

Work Step by Step

f(x) = $(3x + 5)^{3}$ y = $(3x + 5)^{3}$ Solve for x $\sqrt[3] y = 3x + 5$ $\sqrt[3] y - 5 = 3x$ $\frac{\sqrt[3] y - 5}{3} = x$ Interchange x with y $\frac{\sqrt[3] x - 5}{3} = y$ $\frac{\sqrt[3] x - 5}{3} = f^{-1}(x)$
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