Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.3 Inverse, Exponential, and Logarithmic Functions - 1.3 Exercises - Page 36: 31

Answer

$f(x)=8-4x$ $f^{-1}(x)=\dfrac{8-x}{4}$
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Work Step by Step

$f(x)=8-4x$ Substitute $f(x)$ by $y$: $y=8-4x$ Solve the equation for $x$. Start by taking $4x$ to the left side and $y $ to the right side: $4x=8-y$ Take $4$ to divide the right side: $x=\dfrac{8-y}{4}$ Interchange $x$ and $y$: $y=\dfrac{8-x}{4}$ Substitute $y$ by $f^{-1}(x)$: $f^{-1}(x)=\dfrac{8-x}{4}$ The graph of both the function and its inverse is shown in the answer section.
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