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 - 6.1 Functions and Their Inverses - 6.1 Exercises: 42

Answer

$g^{-1}(x) = 4x+3 $

Work Step by Step

$g(x) = \frac{1}{4}x - \frac{3}{4}$ Let $g(x) = y$: $y = \frac{1}{4}x - \frac{3}{4}$. Switch the variables $x$ and $y$ to find the inverse and solve for $y$: $x = \frac{1}{4}y - \frac{3}{4}$ $x = \frac{y}{4}- \frac{3}{4}$ $x + \frac{3}{4}= \frac{y}{4}$ $4x + 3 = y$ $y = 4x + 3$ $g^{-1}(x) = 4x+3 $.
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