Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 6 - Logarithmic Functions - Chapter Review Exercises: 5

Answer

$g^{-1} (x) = \ln \frac{x}{2}$

Work Step by Step

$g(x) = 2e^{x}$ Let $g(x) = y$ $y = 2e^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = 2e^{y}$ $\frac{x}{2} = e^{y}$ $\ln \frac{x}{2} = y$ $g^{-1} (x) = \ln \frac{x}{2}$
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