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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. 282 (page 538)

For function $f (x) = x^{2} - 5 x + 2$ and $g (x) = x^{2} - 3 x - 1$ Find (a) $(f 路 g) (x)$ (b) $(f 路 g) (- 1)$

Short Answer

Expert verified

The solution is (a) $(f 路 g) (x) = x^{4} - 8 x^{3} + 16 x^{2} - x - 2$

(b) $24$

Step by step solution

01

Step 1. Given Information

$f (x) = x^{2} - 5 x + 2$ and $g (x) = x^{2} - 3 x - 1$

02

Part (a) Step 1. Find f·gx

$(f 路 g) (x) = f (x) 路 g (x) (f 路 g) (x) = (x^{2} - 5 x + 2) (x^{2} - 3 x - 1) (f 路 g) (x) = x^{2} (x^{2} - 3 x - 1) - 5 x (x^{2} - 3 x - 1) + 2 (x^{2} - 3 x - 1)$

(a) $(f 路 g) (x) = x^{4} - 8 x^{3} + 16 x^{2} - x - 2$

03

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

$(f 路 g) (x) = x^{4} - 8 x^{3} + 16 x^{2} - x - 2 (f 路 g) (- 1) = {(- 1)}^{4} - 8 {(- 1)}^{3} + 16 {(- 1)}^{2} - (- 1) - 2$

(b) $(f 路 g) (- 1) = 24$

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