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
![### Problem Statement
Let \( f(x) = 2x - 1 \) and \( g(x) = x^2 + 1 \).
Find and simplify: \( (g \circ f) \left( \frac{1}{2} \right) \).
### Answer Choices
Select one:
- A. 1
- B. \(\frac{1}{2}\)
- C. -2
- D. -1
- E. 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0554f3-a7d8-4c12-8db7-464a17f00206%2F087dc06e-3412-44c7-bca0-096d211d7b45%2Fbiy41i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Let \( f(x) = 2x - 1 \) and \( g(x) = x^2 + 1 \).
Find and simplify: \( (g \circ f) \left( \frac{1}{2} \right) \).
### Answer Choices
Select one:
- A. 1
- B. \(\frac{1}{2}\)
- C. -2
- D. -1
- E. 2
![### Functions and Composition: Practice Problem
Consider the functions:
\[ f(x) = x^2 + 3x - 2 \]
\[ g(x) = \sqrt{x + 1} \]
We are asked to find and simplify the composition of functions \((f \circ g)(x)\) evaluated at \(x = 3\).
### Problem:
Find and simplify: \((f \circ g)(3)\)
#### Select one:
- A. \(-8\)
- B. 6
- C. 8
- D. 4
- E. \(-6\)
### Steps to Solve:
1. **Evaluate \(g(3)\):**
\[
g(x) = \sqrt{x + 1}
\]
Substitute \(x = 3\):
\[
g(3) = \sqrt{3 + 1} = \sqrt{4} = 2
\]
2. **Substitute \(g(3)\) into \(f(x)\):**
\[
f(x) = x^2 + 3x - 2
\]
Substitute \(x = 2\):
\[
f(2) = 2^2 + 3 \cdot 2 - 2 = 4 + 6 - 2 = 8
\]
Thus, the correct answer is:
- C. 8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0554f3-a7d8-4c12-8db7-464a17f00206%2F087dc06e-3412-44c7-bca0-096d211d7b45%2Fynytnao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Functions and Composition: Practice Problem
Consider the functions:
\[ f(x) = x^2 + 3x - 2 \]
\[ g(x) = \sqrt{x + 1} \]
We are asked to find and simplify the composition of functions \((f \circ g)(x)\) evaluated at \(x = 3\).
### Problem:
Find and simplify: \((f \circ g)(3)\)
#### Select one:
- A. \(-8\)
- B. 6
- C. 8
- D. 4
- E. \(-6\)
### Steps to Solve:
1. **Evaluate \(g(3)\):**
\[
g(x) = \sqrt{x + 1}
\]
Substitute \(x = 3\):
\[
g(3) = \sqrt{3 + 1} = \sqrt{4} = 2
\]
2. **Substitute \(g(3)\) into \(f(x)\):**
\[
f(x) = x^2 + 3x - 2
\]
Substitute \(x = 2\):
\[
f(2) = 2^2 + 3 \cdot 2 - 2 = 4 + 6 - 2 = 8
\]
Thus, the correct answer is:
- C. 8
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education