Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.2 Inverse Functions - Exercises - Page 334: 1


$f^{-1}(x)= \frac{x+4}{7}$

Work Step by Step

y= 7x-4 or x= $\frac{y+4}{7}$. Thus the inverse is $f^{-1}(y)= \frac{y+4}{7}$. Now, $f^{-1}(f(x))=f^{-1}(7x-4)= \frac{(7x-4)+4}{7}=x$ and $f(f^{-1}(x))=f(\frac{x+4}{7})=7(\frac{x+4}{7})-4=x$ which implies that f is invertible and the inverse is defined as $f^{-1}(x)= \frac{x+4}{7}$.
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