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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 357 (page 1061)

In the following exercises, for each pair of functions, find $(a) (f 鈭� g) (x), (b) (g 鈭� f) (x), (c) (f 路 g) (x)$
$f (x) = 4 x$ and
$g (x) = x^{2} + 3 x$

Short Answer

Expert verified

The answers are

$(a) (f 鈭� g) (x) = 4 x^{2} + 12 x (b) (g 鈭� f) (x) = 16 x^{2} + 12 x (c) (f 路 g) (x) = 4 x^{3} + 12 x^{2}$

Step by step solution

01

Step 1. Given information

The given pair of functions are

$f (x) = 4 x$ and

$g (x) = x^{2} + 3 x$

02

Step 2. Part (a) Solve for f∘g(x)

$(f 鈭� g) (x) = f (g (x)) f (x^{2} + 3 x) = 4 (x^{2} + 3 x) = 4 x^{2} + 12 x$

03

Step 3. Part (b) Solve for g∘f(x)

$(g 鈭� f) (x) = g (4 x) = {(4 x)}^{2} + 3 (4 x) = 16 x^{2} + 12 x$

04

Step 4. Part (c) Solve for f·g(x)

$(f 路 g) (x) = f (x) 路 g (x) = 4 x (x^{2} + 3 x) = 4 x^{3} + 12 x^{2}$

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