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: 45

Answer

$P^{-1}(t) = -\frac{t+7.5}{2.5}$

Work Step by Step

$P(t) = -2.5t -7.5$ Let $P(t) = y$: $y = -2.5t - 7.5$. Switch the variables $t$ and $y$ to find the inverse and solve for $y$: $t = -2.5y - 7.5$ $t+7.5 = -2.5y$ $y = -\frac{t+7.5}{2.5}$ $P^{-1}(t) = -\frac{t+7.5}{2.5}$.
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