Q.369. fx=2x2-4x-7聽and gx=2x2-x+5Find ... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q.369. (page 559)

$f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$

Short Answer

Expert verified

Part (a) The solution is $4 x^{2} - 5 x - 2$ .

Part (b) The solution is $19$ .

Part (c) The solution is $- 3 x - 12$ .

Part (d) The solution is $- 6$ .

Step by step solution

Part (a) Step 1. Given information.

The given polynomial functions are $f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$ .

Part (a) Step 2. Simply the polynomial.

$(f + g) (x) = (2 x^{2} - 4 x - 7) + (2 x^{2} - x + 5) (f + g) (x) = 2 x^{2} + 2 x^{2} - 4 x - x - 7 + 5 (f + g) (x) = 4 x^{2} - 5 x - 2$

Part (a) Step 3. Simplified answer.

Hence, the simplified expression is $(f + g) (x) = 4 x^{2} - 5 x - 2$ .

Part (b) Step 1. Given information.

The given polynomial functions are $f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$ .

Part (b) Step 2. Simplify the function by substituting x=3 in f+gx=4x2-5x-2.

$(f + g) (3) = 4 {(3)}^{2} - 5 (3) - 2 (f + g) (3) = 4 脳 9 - 15 - 2 (f + g) (3) = 36 - 15 - 2 (f + g) (3) = 36 - 17 (f + g) (3) = 19$

Part (c) Step 3. Simplified answer.

Hence, the simplified value is $(f + g) (3) = 19$ .

Part (c) Step 1. Given information.

The given polynomial functions are $f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$ .

Part (c) Step 2. Simplify the polynomial function.

$(f - g) (x) = (2 x^{2} - 4 x - 7) - (2 x^{2} - x + 5) (f - g) (x) = 2 x^{2} - 2 x^{2} - 4 x + x - 7 - 5 (f - g) (x) = - 3 x - 12$

Part (c) Step 3. Simplified answer.

Hence, the simplified polynomial is $(f - g) (x) = - 3 x - 12$ .

Part (d) Step 1. Given information.

The given polynomials are $f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$ .

Part (d) Step 2. Simplify the polynomials by substituting x=-2 in f-gx=-3x-12.

$(f - g) (- 2) = - 3 (- 2) - 12 (f - g) (- 2) = 6 - 12 (f - g) (- 2) = - 6$

Part (d) Step 3. Simplified answer.

Hence, the simplified value is $(f - g) (- 2) = - 6$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

$f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Simply the polynomial.

Part (a) Step 3. Simplified answer.

Part (b) Step 1. Given information.

Part (b) Step 2. Simplify the function by substituting x=3 in f+gx=4x2-5x-2.

Part (c) Step 3. Simplified answer.

Part (c) Step 1. Given information.

Part (c) Step 2. Simplify the polynomial function.

Part (c) Step 3. Simplified answer.

Part (d) Step 1. Given information.

Part (d) Step 2. Simplify the polynomials by substituting x=-2 in f-gx=-3x-12.

Part (d) Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

91影视

fx=2x2-4x-7and gx=2x2-x+5Find (a) f+gx(b) f+g3(c) f-gx(d)f-g-2

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Simply the polynomial.

Part (a) Step 3. Simplified answer.

Part (b) Step 1. Given information.

Part (b) Step 2. Simplify the function by substituting x=3 in f+gx=4x2-5x-2.

Part (c) Step 3. Simplified answer.

Part (c) Step 1. Given information.

Part (c) Step 2. Simplify the polynomial function.

Part (c) Step 3. Simplified answer.

Part (d) Step 1. Given information.

Part (d) Step 2. Simplify the polynomials by substituting x=-2 in f-gx=-3x-12.

Part (d) Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

$f (x) = 2 x^{2} - 4 x - 7$ and $g (x) = 2 x^{2} - x + 5$
Find (a) $(f + g) (x)$ (b) $(f + g) (3)$ (c) $(f - g) (x)$ (d) $(f - g) (- 2)$