College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.1 - Composite Functions - 6.1 Assess Your Understanding - Page 409: 24


$ a.\qquad (f\circ g)(x)=-2x+4,\qquad$ Domain: $\mathbb{R}$ $ b.\qquad (g\circ f)(x)=-2x-4,\qquad$ Domain: $\mathbb{R}$ $ c.\qquad (f\circ f)(x)=x,\qquad$ Domain: $\mathbb{R}$ $ d.\qquad(g\circ g)(x)=4x-12,\qquad$ Domain: $\mathbb{R}$

Work Step by Step

$ f(x)=-x,\qquad$ Domain: $\mathbb{R}$ $ g(x)=2x-4,\qquad$ Domain: $\mathbb{R}$ $a.$ $f\circ g(x)=f[g(x)]=-g(x)$ $=-(2x-4)$ $=-2x+4,\qquad$ Domain: $\mathbb{R}$ $b.$ $(g\circ f)(x)=g[f(x)] =2f(x)-4$ $=2(-x)-4$ $=-2x-4,\qquad$ Domain: $\mathbb{R}$ $c.$ $f\circ f(x)=f[f(x)]=-f(x)$ $=-(-x)$ $=x,\qquad$ Domain: $\mathbb{R}$ $d.$ $(g\circ g)(x)=g[g(x)] =2g(x)-4$ $=2(2x-4)-4$ $=4x-8-4$ $=4x-12,\qquad$ Domain: $\mathbb{R}$
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