Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.2 - Composite and Inverse Functions - Exercise Set - Page 690: 101

Answer

True.

Work Step by Step

The given functions are $f(x)=\sqrt x$ and $g(x)=2x-1$. Plug $x=5$ into the second function. $g(5)=2(5)-1$ $g(5)=10-1$ $g(5)=9$. $(f\circ g)(5)=f(g(5))$ $(f\circ g)(5)=f(9)$ Plug $x=9$ into first function. $(f\circ g)(5)=\sqrt 9$ $(f\circ g)(5)=3$. Now plug $x=2$ into the second function. $g(2)=2(2)-1$ $g(2)=4-1$ $g(2)=3$. Hence, $(f\circ g)(5)=g(2)=3$.
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