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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. 5.70 (page 535)

For function $f (x) = x - 7$ and $g (x) = x^{2} + 8 x + 4$ . Find (a) $(f 路 g) (x)$ (b) $(f 路 g) (2)$

Short Answer

Expert verified

(a) $(f 路 g) (x) = x^{3} + x^{2} - 52 x - 28$

(b) $(f 路 g) (2) = - 120$

Step by step solution

01

Step 1. Given Information

Given functions $f (x) = x - 7$ and $g (x) = x^{2} + 8 x + 4$ .

We need to find $(f 路 g) (x) a n d (f 路 g) (2)$

02

Part (a) Step 1. Finding f·gx

$(f 路 g) (x) = f (x) g (x) = (x - 7) (x^{2} + 8 x + 4) (f 路 g) (x) = x^{3} + 8 x^{2} + 4 x - 7 x^{2} - 56 x - 28 (f 路 g) (x) = x^{3} + x^{2} - 52 x - 28$

03

Part (b) Step 1. Finding f·g2

$(f 路 g) (x) = x^{3} + x^{2} - 52 x - 28 (f 路 g) (2) = 2^{3} + 2^{2} - 52 (2) - 28 (f 路 g) (2) = 8 + 4 - 104 - 28 (f 路 g) (2) = 12 - 132 = - 120$

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