Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 787: 9

Answer

$a.\quad 5$ $b.\quad-1$ $c.\quad x^{2}-6x+10$ $d.\quad x^{2}-2$

Work Step by Step

$(f\circ g)(x)=f[g(x)]=[g(x)]^{2}+1$ $=(x-3)^{2}+1$ $=x^{2}-6x+9+1$ $=x^{2}-6x+10 \qquad ... \quad(c)$ $(f\circ g)(1)=1^{2}-6(1)+10=5 \qquad ... \quad(a)$ $(g\circ f)(x)=g[f(x)]=f(x)-3$ $=x^{2}+1-3$ $=x^{2}-2 \qquad ... \quad(d)$ $(g\circ f)(1)=1^{2}-2=-1 \qquad ... \quad(b)$
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