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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.329. (page 552)

For functions $f (x) = x^{2} + 4 x - 3$ and $g (x) = x^{2} + 2 x + 4$ .
Find (a) $(f 路 g) (x)$ and (b) $(f 路 g) (1)$ .

Short Answer

Expert verified

Part (a). The solution is $x^{4} + 6 x^{3} + 9 x^{2} + 10 x - 12$ .

Part (b). The solution is $14$ .

Step by step solution

01

Part (a). Step 1. Given information.

The function $f (x) = x^{2} + 4 x - 3$ and $g (x) = x^{2} + 2 x + 4$ .

02

Part (a). Step 2. To multiply the polynomial function, by substituting the value of fx and gx.

Solve it as follows:

$(f 路 g) (x) = f (x) 路 g (x) 鈬� (x^{2} + 4 x - 3) 路 (x^{2} + 2 x + 4) 鈬� x^{2} (x^{2} + 2 x + 4) + 4 x (x^{2} + 2 x + 4) - 3 (x^{2} + 2 x + 4) 鈬� x^{4} + 2 x^{3} + 4 x^{2} + 4 x^{3} + 8 x^{2} + 16 x - 3 x^{2} - 6 x - 12 鈬� x^{4} + 6 x^{3} + 9 x^{2} + 10 x - 12$

03

Part (a). Step 3. Simplified answer.

Hence, the obtained result is $x^{4} + 6 x^{3} + 9 x^{2} + 10 x - 12$ .

04

Part (b). Step 1. Given information.

The function $f (x) = x^{2} + 4 x - 3$ and $g (x) = x^{2} + 2 x + 4$ .

05

Part (b). Step 2. To find the value of f·g1 by substituting the value of x=1 in f·gx=x4+6x3+9x2+10x-12.

Solve it as follows:

$(f 路 g) (1) = {(1)}^{4} + 6 {(1)}^{3} + 9 {(1)}^{2} + 10 (1) - 12 鈬� 1 + 6 + 9 + 10 - 12 鈬� 14$

06

Part (b). Simplified answer.

Hence, the simplified expression is $14$ .

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