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 - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 279: 13


(a) $97$ (b) $-\dfrac{163}{2}$ (c) $1$ (d) $-\dfrac{3}{2}$

Work Step by Step

a) $(f\circ g)(4)= f(g(4))=f(3-\frac{1}{2}\times4^{2})=f(-5)=4(-5)^{2}-3=97$ b) $(g\circ f)(2)=g(f(2))=g(4\times2^{2}-3)=g(13)=3-\frac{1}{2}\times13^{2}=-\dfrac{163}{2}$ c) $(f\circ f)(1)=f(f(1))=f(4\times1^{2}-3)=f(1)=4\times1^{2}-3=1$ d) $(g\circ g)(0)=g(g(0))=g(3-\frac{1}{2}\times0^{2})=g(3)=3-\frac{1}{2}\times3^{2}=-\dfrac{3}{2}$
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