Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.2 - Inverse Functions - Exercise Set: 35

Answer

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

Work Step by Step

$f(x)=\dfrac{5}{3x+1}$ Replace $f(x)$ with $y$: $y=\dfrac{5}{3x+1}$ Interchange $x$ and $y$: $x=\dfrac{5}{3y+1}$ Solve for $y$. Begin by taking $3y+1$ to multiply the left side: $(3y+1)x=5$ Take $x$ to divide the right side: $3y+1=\dfrac{5}{x}$ Take the $1$ to the right side: $3y=\dfrac{5}{x}-1$ Take the $3$ to divide the right side: $y=\dfrac{5}{3x}-\dfrac{1}{3}$ Replace $y$ with $f^{-1}(x)$: $f^{-1}(x)=\dfrac{5}{3x}-\dfrac{1}{3}$
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