Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Chapter Review - Review Exercises - Page 370: 4

Answer

(a) $ e^4$. (b) $ 3e^{-2}-2 $. (c) $ e^{e^4}$. (d) $ -17$.

Work Step by Step

Given $f(x)=e^x$ and $g(x)=3x-2$, we have: (a) $(f\circ g)(2)=f(3(2)-2)=f(4)=e^4$. (b) $(g\circ f)(-2)=g(e^{-2})=3e^{-2}-2 $. (c) $(f\circ f)(4)=f(e^4)=e^{e^4}$. (d) $(g\circ g)(-1)=g(3(-1)-2)=g(-5)=3(-5)-2=-17$.
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