Q5.69 For function聽f(x)=x-5聽and聽g(x... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q5.69 (page 535)

For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$

Short Answer

Expert verified

$(a) M u l t i p l y t h e g i v e n b i n o m i a l f u n c t i o n (f . g) (x) = (x - 5) (x^{2} - 2 x + 3) = x^{3} - 7 x^{2} + 13 x - 15 (b) M u l t i p l y t h e g i v e n b i n o m i a l f u n c t i o n (f . g) (2) = (x - 5) (x^{2} - 2 x + 3) = (2 - 5) (2^{2} - 2 脳 2 + 3) = - 9$

Step by step solution

Step 1

Given information:

$f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3$

Step 2

Multiplying polynomials require only three steps.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.
Add the powers of the same variables using the exponent rule.
Then, simplify the resulting polynomial by adding or subtracting the like terms.

Step 3Part(a) Step1. Multiply the Polynomials

$p a r t (a) S t e p 1 . M u l t i p l y t h e p o l y n o m i a l s (a) (f . g) (x) = f (x) . g (x) S u b t i t u t e f o r f (x) a n d g (x) (f . g) (x) = (x - 5) (x^{2} - 2 x + 3) M u l t i p l y t h e p o l y n o m i a l s (f . g) (x) = x (x^{2} - 2 x + 5) - 5 (x^{2} - 2 x + 3) D i s t r i b u t e (f . g) (x) = x^{3} - 2 x^{2} + 5 x - 5 x^{2} + 10 x - 15 C o m b i n e l i k e t e r m s (f . g) (x) = x^{3} - 7 x^{2} + 15 x - 15$

Part(b) Step1. Multiply the Polynomials

$(b) I n p a r t (a) w e f o u n d (f . g) (x) a n d n o w a s k e d t o f i n d (f . g) (2) (f . g) (x) = x^{3} - 7 x^{2} + 15 x - 15 t o f i n d (f . g) (2) s u b t i t u t e x = 2 (f . g) (2) = {(2)}^{3} - 7 {(2)}^{2} + 15 (2) - 15 (f . g) (2) = 8 - 28 + 30 - 15 (f . g) (2) = - 5$

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91影视

For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$

Short Answer

Step by step solution

Step 1

Step 2

Step 3Part(a) Step1. Multiply the Polynomials

Part(b) Step1. Multiply the Polynomials

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91影视

For functionf(x)=x-5andg(x)=x2-2x+3,Find(a)(f.g)(x)(b)(f.g)(2)

Short Answer

Step by step solution

Step 1

Step 2

Step 3Part(a) Step1. Multiply the Polynomials

Part(b) Step1. Multiply the Polynomials

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

For function $f (x) = x - 5 a n d g (x) = x^{2} - 2 x + 3, F i n d (a) (f . g) (x) (b) (f . g) (2)$