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: 4

Answer

$f^{-1}(x) = \log_6 (\frac{x}{3.5} )$

Work Step by Step

$f(x) = 3.5(6)^{x}$ Let $f(x) = y$ $y = 3.5(6)^{x}$ Swap the variables $x$ and $y$ and then solve for $y$ to find the inverse: $x = 3.5(6)^{y}$ $\frac{x}{3.5} = (6)^{y}$ $y = \log_6 (\frac{x}{3.5} )$ $f^{-1}(x) = \log_6 (\frac{x}{3.5} )$
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