Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - Chapter Review - Review Exercises - Page 345: 2

Answer

(a) $ \sqrt {11}$ (b) $ 1$ (c) $ \sqrt {\sqrt 6+2}$ (d) $ 19$

Work Step by Step

Given $f(x)=\sqrt {x+2}$ and $g(x)=2x^2+1$, we have (a) $(f\circ g)(2)=f(g(2))=f(2(2)^2+1)=f(9)=\sqrt {9+2}=\sqrt {11}$ (b) $(g\circ f)(-2)=g(f(-2))=g(\sqrt {-2+2})=g(0)=2(0)^2+1=1$ (c) $(f\circ f)(4)=f(f(4))=f(\sqrt {4+2})=f(\sqrt 6)=\sqrt {\sqrt 6+2}$ (d) $(g\circ g)(-1)=g(g(-1))=g(2(-1)^2+1)=g(3)=2(3)^2+1=19$
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