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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q 280 (page 538)

For function $f (x) = 2 x - 7$ and $g (x) = 2 x + 7$
find (a) $(f 路 g) (x)$ (b) $(f 路 g) (- 3)$

Short Answer

Expert verified

The solution is (a) $4 x^{2} - 49$ (b) $- 13$

Step by step solution

01

Step 1. Given information

$f (x) = 2 x - 7$ and $g (x) = 2 x + 7$

02

Part (a) Step 1. Find f·gx

Substitute for, $f (x)$ and $g (x)$ and multiply the polynomials.

$(f 路 g) (x) = f (x) 路 g (x) (f 路 g) (x) = (2 x - 7) (2 x + 7) (f 路 g) (x) = 2 x (2 x + 7) - 7 (2 x + 7)$

apply the difference of two squares formula

$(f 路 g) (x) = {(2 x)}^{2} - 7^{2}$

Simplify

(a) $(f 路 g) (x) = 4 x^{2} - 49$

03

Part (b) Step 1. Substitute x=-3

Substitute $x = - 3$ and simplify.

In part (a) we found $(f 路 g) (x)$ and now are asked to find $(f 路 g) (- 3)$

To find $(f 路 g) (- 3)$ substitute $x = - 3$

$(f 路 g) (x) = 4 x^{2} - 49 (f 路 g) (- 3) = 4 {(- 3)}^{2} - 49$

(b) $(f 路 g) (- 3) = - 13$

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