**Example Question for Educational Website** ***Question 11*** Let \( f(x) = 4x + 3 \) and \( g(x) = 4x^2 + 3x \). After simplifying, \[ (f + g)(x) = \] _______________ **Question Help:** [Video] *Submit Question Button* This image contains a mathematical problem aimed at helping students to practice their understanding of function addition. The objective is to determine the expression for \((f + g)(x)\) by adding the given functions \(f(x)\) and \(g(x)\). ### Explanation: 1. **Definition of Functions:** - \( f(x) = 4x + 3 \) - \( g(x) = 4x^2 + 3x \) 2. **Addition of Functions:** - The sum of \( f(x) \) and \( g(x) \) is given by: \[ (f + g)(x) = f(x) + g(x) \] 3. **Simplifying:** - Substitute the expressions for \( f(x) \) and \( g(x) \): \[ (f + g)(x) = (4x + 3) + (4x^2 + 3x) \] - Combine like terms (if any): \[ (f + g)(x) = 4x^2 + 4x + 3 + 3x \] - Simplify further: \[ (f + g)(x) = 4x^2 + 7x + 3 \] #### Diagram Explanation: The provided content does not have any graphs or diagrams. If there were accompanying visuals, they might typically show the functions \( f(x) \) and \( g(x) \), and their sum graphically to aid in understanding how the combined function behaves. However, none are present here.
**Example Question for Educational Website** ***Question 11*** Let \( f(x) = 4x + 3 \) and \( g(x) = 4x^2 + 3x \). After simplifying, \[ (f + g)(x) = \] _______________ **Question Help:** [Video] *Submit Question Button* This image contains a mathematical problem aimed at helping students to practice their understanding of function addition. The objective is to determine the expression for \((f + g)(x)\) by adding the given functions \(f(x)\) and \(g(x)\). ### Explanation: 1. **Definition of Functions:** - \( f(x) = 4x + 3 \) - \( g(x) = 4x^2 + 3x \) 2. **Addition of Functions:** - The sum of \( f(x) \) and \( g(x) \) is given by: \[ (f + g)(x) = f(x) + g(x) \] 3. **Simplifying:** - Substitute the expressions for \( f(x) \) and \( g(x) \): \[ (f + g)(x) = (4x + 3) + (4x^2 + 3x) \] - Combine like terms (if any): \[ (f + g)(x) = 4x^2 + 4x + 3 + 3x \] - Simplify further: \[ (f + g)(x) = 4x^2 + 7x + 3 \] #### Diagram Explanation: The provided content does not have any graphs or diagrams. If there were accompanying visuals, they might typically show the functions \( f(x) \) and \( g(x) \), and their sum graphically to aid in understanding how the combined function behaves. However, none are present here.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Example Question for Educational Website**
***Question 11***
Let \( f(x) = 4x + 3 \) and \( g(x) = 4x^2 + 3x \).
After simplifying,
\[ (f + g)(x) = \]
_______________
**Question Help:** [Video]
*Submit Question Button*
This image contains a mathematical problem aimed at helping students to practice their understanding of function addition. The objective is to determine the expression for \((f + g)(x)\) by adding the given functions \(f(x)\) and \(g(x)\).
### Explanation:
1. **Definition of Functions:**
- \( f(x) = 4x + 3 \)
- \( g(x) = 4x^2 + 3x \)
2. **Addition of Functions:**
- The sum of \( f(x) \) and \( g(x) \) is given by:
\[
(f + g)(x) = f(x) + g(x)
\]
3. **Simplifying:**
- Substitute the expressions for \( f(x) \) and \( g(x) \):
\[
(f + g)(x) = (4x + 3) + (4x^2 + 3x)
\]
- Combine like terms (if any):
\[
(f + g)(x) = 4x^2 + 4x + 3 + 3x
\]
- Simplify further:
\[
(f + g)(x) = 4x^2 + 7x + 3
\]
#### Diagram Explanation:
The provided content does not have any graphs or diagrams. If there were accompanying visuals, they might typically show the functions \( f(x) \) and \( g(x) \), and their sum graphically to aid in understanding how the combined function behaves. However, none are present here.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd21c4d6b-d29a-46fe-bc39-340308e97d91%2F6f34511e-0584-435b-ac4a-cc5de43db18a%2Fqqu6ilg.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Question for Educational Website**
***Question 11***
Let \( f(x) = 4x + 3 \) and \( g(x) = 4x^2 + 3x \).
After simplifying,
\[ (f + g)(x) = \]
_______________
**Question Help:** [Video]
*Submit Question Button*
This image contains a mathematical problem aimed at helping students to practice their understanding of function addition. The objective is to determine the expression for \((f + g)(x)\) by adding the given functions \(f(x)\) and \(g(x)\).
### Explanation:
1. **Definition of Functions:**
- \( f(x) = 4x + 3 \)
- \( g(x) = 4x^2 + 3x \)
2. **Addition of Functions:**
- The sum of \( f(x) \) and \( g(x) \) is given by:
\[
(f + g)(x) = f(x) + g(x)
\]
3. **Simplifying:**
- Substitute the expressions for \( f(x) \) and \( g(x) \):
\[
(f + g)(x) = (4x + 3) + (4x^2 + 3x)
\]
- Combine like terms (if any):
\[
(f + g)(x) = 4x^2 + 4x + 3 + 3x
\]
- Simplify further:
\[
(f + g)(x) = 4x^2 + 7x + 3
\]
#### Diagram Explanation:
The provided content does not have any graphs or diagrams. If there were accompanying visuals, they might typically show the functions \( f(x) \) and \( g(x) \), and their sum graphically to aid in understanding how the combined function behaves. However, none are present here.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education