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: 23


$ a.\qquad (f\circ g)(x)=6x+3,\qquad$ Domain: $\mathbb{R}$ $ b.\qquad (g\circ f)(x)=6x+9,\qquad$ Domain: $\mathbb{R}$ $ c.\qquad (f\circ f)(x)=4x+9,\qquad$ Domain: $\mathbb{R}$ $ d.\qquad(g\circ g)(x)=9x,\qquad$ Domain: $\mathbb{R}$

Work Step by Step

$ f(x)=2x+3,\qquad$ Domain: $\mathbb{R}$ $ g(x)=3x,\qquad$ Domain: $\mathbb{R}$ $a.$ $f\circ g(x)=f[g(x)]=2g(x)+3$ $=2(3x)+3$ $=6x+3,\qquad$ Domain: $\mathbb{R}$ $b.$ $(g\circ f)(x)=g[f(x)] =3f(x)$ $=3(2x+3)$ $=6x+9,\qquad$ Domain: $\mathbb{R}$ $c.$ $f\circ f(x)=f[f(x)]=2f(x)+3$ $=2(2x+3)+3$ $=4x+6+3$ $=4x+9,\qquad$ Domain: $\mathbb{R}$ $d.$ $(g\circ g)(x)=g[g(x)] =3g(x)$ $=3(3x)$ $=9x,\qquad$ Domain: $\mathbb{R}$
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