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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.328. (page 552)

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

Short Answer

Expert verified

Part (a). The solution is $x^{4} - 8 x^{3} + 16 x^{2} - x - 2$ .

Part (b). The solution is localid="1644479151190" $24$ .

Step by step solution

01

Part (a). Step 1. Given information.

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

02

Part (a). Step 2. Multiply the polynomial functions.

$(f 路 g) (x) = f (x) 路 g (x) 鈬� (x^{2} - 5 x + 2) 路 (x^{2} - 3 x - 1) 鈬� x^{2} (x^{2} - 3 x - 1) - 5 x (x^{2} - 3 x - 1) + 2 (x^{2} - 3 x - 1) 鈬� x^{4} - 3 x^{3} - x^{2} - 5 x^{3} + 15 x^{2} + 5 x + 2 x^{2} - 6 x - 2 鈬� x^{4} - 8 x^{3} + 16 x^{2} - x - 2$

03

Part (a). Step 3. Simplified answer.

Hence, the obtained result is $x^{4} - 8 x^{3} + 16 x^{2} - x - 2$ . $x^{4} - 8 x^{3} + 16 x^{2} - x - 2$

04

Part (b). Given information.

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

05

Part (b). Step 2. To find the value of f·g-1 by substituting x=-1 in f·gx=x4-8x3+16x2-x-2

Solve it as follows:

$(f 路 g) (- 1) = {(- 1)}^{4} - 8 {(- 1)}^{3} + 16 {(- 1)}^{2} - (- 1) - 2 鈬� 1 - 8 (- 1) + 16 + 1 - 2 鈬� 1 + 8 + 16 - 1 鈬� 24$

06

Part (b). Simplified answer.

Hence, the simplified expression is $24$ .

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Most popular questions from this chapter

Multiply (a) $(2 脳 10^{2}) (1 脳 10^{- 4})$ to get answer in decimal form

Divide (b) $\frac{5 脳 10^{- 2}}{1 脳 10^{- 10}}$ to get answer in decimal form

Add or subtract: $(a) - 15 c^{2} + 8 c^{2} (b) - 15 y^{2} z^{3} - (- 5 y^{2} z^{3})$

$Find the sum: (14 y^{2} + 6 y - 4) + (3 y^{2} + 8 y + 5)$

Multiply each pair of conjugates using the product of the conjugates pattern.

$(8 j + 4) (8 j - 4)$

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