Chapter 5: Q. 5.22 (page 496)

$Forfunctions f (x) = 5 x^{2} - 4 x - 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f - g) (x) (d) (f - g) (- 2) .$

Short Answer

Expert verified

The value is

$\begin{array}{l} (a) (f + g) (x) = 6 x^{2} - x + 7 \\ (b) (f + g) (3) = 58 \\ (c) (f - g) (x) = 4 x^{2} - 7 x - 9 \\ (d) (f - g) (- 2) = 21 \end{array}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenfunctionsare \\ f (x) = 5 x^{2} - 4 x - 1 \\ g (x) = x^{2} + 3 x + 8 \\ (a) (f + g) (x) (b) (f + g) (3) (c) (f - g) (x) (d) (f - g) (- 2) \end{array}$

Step 2. Solve for part (a)

$\begin{array}{l} Weknow (f + g) (x) = f (x) + g (x) \\ Substitutethefunctions f (x) and g (x) \\ \Rightarrow (f + g) (x) = (5 x^{2} - 4 x - 1) + (x^{2} + 3 x + 8) \\ = 5 x^{2} - 4 x - 1 + x^{2} + 3 x + 8 [Rewritewithoutparentheses] \\ = 5 x^{2} + x^{2} - 4 x + 3 x - 1 + 8 [Putliketermstogether] \\ = 6 x^{2} - x + 7 \end{array}$

Step 3. Solve for part (b)

$\begin{array}{l} Wehave (f + g) (x) = 6 x^{2} - x + 7 \\ \Rightarrow (f + g) (3) = 6 {(3)}^{2} - (3) + 7 [Substitute x = 3] \\ = 6 (9) - 3 + 7 \\ = 54 - 3 + 7 \\ = 58 \end{array}$

Step 4. Solve for part (c)

$\begin{array}{l} Weknow (f - g) (x) = f (x) - g (x) \\ Substitutethefunctions f (x) and g (x) \\ \Rightarrow (f - g) (x) = (5 x^{2} - 4 x - 1) - (x^{2} + 3 x + 8) \\ = 5 x^{2} - 4 x - 1 - x^{2} - 3 x - 8 [Rewritewithoutparentheses] \\ = 5 x^{2} - x^{2} - 4 x - 3 x - 1 - 8 [Putliketermstogether] \\ = 4 x^{2} - 7 x - 9 \end{array}$

Step 4. Solve for part (d)

$\begin{array}{l} Wehave (f - g) (x) = 4 x^{2} - 7 x - 9 \\ \Rightarrow (f - g) (- 2) = 4 x^{2} - 7 x - 9 [Substitute x = 2] \\ = 4 {(2)}^{2} - 7 (- 2) - 9 \\ = 4 (4) + 14 - 9 \\ = 16 + 14 - 9 \\ = 21 \end{array}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$Forfunctions f (x) = 5 x^{2} - 4 x - 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f - g) (x) (d) (f - g) (- 2) .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for part (a)

Step 3. Solve for part (b)

Step 4. Solve for part (c)

Step 4. Solve for part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Forfunctionsf(x)=5x2−4x−1andg(x)=x2+3x+8,find(a)(f+g)(x)(b)(f+g)(3)(c)(f−g)(x)(d)(f−g)(−2).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve for part (a)

Step 3. Solve for part (b)

Step 4. Solve for part (c)

Step 4. Solve for part (d)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

$Forfunctions f (x) = 5 x^{2} - 4 x - 1 and g (x) = x^{2} + 3 x + 8, find (a) (f + g) (x) (b) (f + g) (3) (c) (f - g) (x) (d) (f - g) (- 2) .$