Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.1 Inverse Functions - 6.1 Exercises - Page 407: 29

Answer

$f^{-1}(x)=\frac{x^{2}-3}{4}$
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Work Step by Step

Calculate the inverse of the function $f(x)=\sqrt {4x+3}$ Write $y=f(x)$ $y=\sqrt {4x+3}$ Solve this equation for x in terms of y to get the inverse function. $x=\frac{y^{2}-3}{4}$ To express $f^{-1}(x)$ as a function of x,interchange x and y. The resulting equation is $y=\frac{x^{2}-3}{4}$ Therefore, the inverse of the function $f^{-1}(x)=y=\frac{x^{2}-3}{4}$ The graph of the functions $f(x)=\sqrt {4x+3}$ and $f^{-1}(x)=\frac{x^{2}-3}{4}$ along the line $y=x$ on the same screen is depicted below:
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