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 - 6.2 Logarithmic Functions - 6.2 Exercises: 96

Answer

$f^{-1}(t) = \log_2 3t$

Work Step by Step

$f(t) = \frac{1}{3}(2)^{t}$ Let $f(t) = y$ $y = \frac{1}{3}(2)^{t}$ Swap the $t$ and $y$ variable to find the inverse: $t = \frac{1}{3}(2)^{y}$ $t = \frac{2^{y}}{3}$ $3t = 2^{y}$ $y = \log_2 3t$ $f^{-1}(t) = \log_2 3t$
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