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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. 279 (page 538)

For function $f (x) = x - 1$ and $g (x) = 4 x^{2} + 3 x - 5$ find (a) $(f 路 g) (x)$ (b ) $(f 路 g) (- 2)$

Short Answer

Expert verified

The solution is (a) $4 x^{3} - x^{2} - 8 x + 5$ (b) $- 15$

Step by step solution

01

Step 1. Given information

$f (x) = x - 1$ and $g (x) = 4 x^{2} + 3 x - 5$

02

Part (a) Step 1. Find f·gx

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

$(f 路 g) (x) = f (x) 路 g (x) (f 路 g) (x) = (x - 1) (4 x^{2} + 3 x - 5) (f 路 g) (x) = x (4 x^{2} + 3 x - 5) - 1 (4 x^{2} + 3 x - 5)$

distribute the parenthesis

$(f 路 g) (x) = x (4 x^{2} + 3 x - 5) - 1 (4 x^{2} + 3 x - 5) (f 路 g) (x) = x 路 4 x^{2} + x 路 3 x + x (- 5) - 1 路 3 x - 1 路 (- 5)$

Simplify

(a) $(f 路 g) (x) = 4 x^{3} - x^{2} - 8 x + 5$

03

Part (b) Step 1. Substitute x=-2

Substitute $x = - 2$ and simplify

In part (a) we found $(f 路 g) (x)$ and now are asked to find $(f 路 g) (- 2)$

To find $(f 路 g) (- 2)$ substitute $x = - 2$

role="math" localid="1646649914877" $(f 路 g) (x) = 4 x^{3} - x^{2} - 8 x + 5 (f 路 g) (- 2) = 4 {(- 2)}^{3} - {(- 2)}^{2} - 8 (- 2) + 5$

(b) $(f 路 g) (- 2) = - 15$

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Most popular questions from this chapter

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative

Multiply (a) $(3 脳 10^{- 5}) (3 脳 10^{9})$ to get answer in decimal form

Divide (b) $\frac{7 脳 10^{- 3}}{1 脳 10^{- 7}}$ 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 product of the below expression.

${(t - 9)}^{2}$

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

$(m + \frac{2}{3} n) (m - \frac{2}{3} n)$

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