Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 227: 58

Answer

$f^{-1}(x)=-\dfrac{x+2}{3x-4}$

Work Step by Step

$f(x)=\dfrac{4x-2}{3x+1}$ Rewrite this expression as $y=\dfrac{4x-2}{3x+1}$ and solve for $x$: $y=\dfrac{4x-2}{3x+1}$ Take $3x+1$ to multiply the left side: $y(3x+1)=4x-2$ $3xy+y=4x-2$ Take $4x$ to the left side and $y$ to the right side: $3xy-4x=-2-y$ Take common factor $x$ from the left side: $x(3y-4)=-2-y$ Take $3y-4$ to divide the right side: $x=\dfrac{-2-y}{3y-4}$ $x=-\dfrac{y+2}{3y-4}$ Interchange $x$ and $y$: $y=-\dfrac{x+2}{3x-4}$ The inverse of the original function is $f^{-1}(x)=-\dfrac{x+2}{3x-4}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.