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: 41

Answer

$f^{-1}(x) = 5x - 3$

Work Step by Step

$f(x) = \frac{1}{5}x + \frac{3}{5}$ Let $f(x) = y$: $y = \frac{1}{5}x + \frac{3}{5}$ Switch the variables $x$ and $y$ to find the inverse and solve for $y$: $x = \frac{1}{5}y + \frac{3}{5}$ $x = \frac{y}{5} + \frac{3}{5}$ $x-\frac{3}{5} = \frac{y}{5} $ $5x - \frac{15}{5} = y$ $y = 5x - 3$ $f^{-1}(x) = 5x - 3$
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