Use the graph to evaluate the expressions (fog)(1)and (gof)(3). (fog)(1) = O y = f(x) 10 ₹ 8- 6 -10-8-6-4-261 -6- -8- 10 y=g(x) 6 8 10
Use the graph to evaluate the expressions (fog)(1)and (gof)(3). (fog)(1) = O y = f(x) 10 ₹ 8- 6 -10-8-6-4-261 -6- -8- 10 y=g(x) 6 8 10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![---
**Title: Evaluating Composite Functions Using Graphs**
**Instructions:**
Use the graph to evaluate the expressions \((f \circ g)(1)\) and \((g \circ f)(3)\).
**Section: Composite Function Evaluation**
\((f \circ g)(1) =\) [Input Box]
**Graph Explanation:**
- The graph is a coordinate plane with two functions plotted:
- **\(y = f(x)\)**: represented by a blue line with a positive slope.
- **\(y = g(x)\)**: represented by another blue line with a negative slope.
- The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10, with each major grid line representing an interval of 2.
- **Intersection Points:** The lines cross each other at a specific point, which may be critical for solving the expressions.
- **Objective:** Use the graph lines to find the values of \(f(g(1))\) and \(g(f(3))\).
**Guidance:**
1. **Find \(g(1)\):**
- Locate \(x = 1\) on the x-axis.
- Follow the vertical line up to the line representing \(y = g(x)\).
- Read the y-coordinate of the intersection to find \(g(1)\).
2. **Find \(f(g(1))\):**
- Use the value of \(g(1)\) as the new input for \(f(x)\).
- Follow the horizontal line to the line representing \(y = f(x)\).
- Read the y-coordinate to find the value of \(f(g(1))\).
3. **Find \(f(3)\):**
- Locate \(x = 3\) on the x-axis.
- Follow the vertical line up to the line representing \(y = f(x)\).
- Read the y-coordinate of the intersection to find \(f(3)\).
4. **Find \(g(f(3))\):**
- Use the value of \(f(3)\) as the new input for \(g(x)\).
- Follow the horizontal line to the line representing \(y = g(x)\).
- Read the y-coordinate to find the value of \(g(f(3))\).
Fill in the evaluated values in the respective input boxes.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8fa05ee-52b8-4b3d-a3d0-54c9685a9d54%2F12d848b0-0e2e-4059-ba9d-c7a2a1224bd0%2F0yt2x7k_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Title: Evaluating Composite Functions Using Graphs**
**Instructions:**
Use the graph to evaluate the expressions \((f \circ g)(1)\) and \((g \circ f)(3)\).
**Section: Composite Function Evaluation**
\((f \circ g)(1) =\) [Input Box]
**Graph Explanation:**
- The graph is a coordinate plane with two functions plotted:
- **\(y = f(x)\)**: represented by a blue line with a positive slope.
- **\(y = g(x)\)**: represented by another blue line with a negative slope.
- The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10, with each major grid line representing an interval of 2.
- **Intersection Points:** The lines cross each other at a specific point, which may be critical for solving the expressions.
- **Objective:** Use the graph lines to find the values of \(f(g(1))\) and \(g(f(3))\).
**Guidance:**
1. **Find \(g(1)\):**
- Locate \(x = 1\) on the x-axis.
- Follow the vertical line up to the line representing \(y = g(x)\).
- Read the y-coordinate of the intersection to find \(g(1)\).
2. **Find \(f(g(1))\):**
- Use the value of \(g(1)\) as the new input for \(f(x)\).
- Follow the horizontal line to the line representing \(y = f(x)\).
- Read the y-coordinate to find the value of \(f(g(1))\).
3. **Find \(f(3)\):**
- Locate \(x = 3\) on the x-axis.
- Follow the vertical line up to the line representing \(y = f(x)\).
- Read the y-coordinate of the intersection to find \(f(3)\).
4. **Find \(g(f(3))\):**
- Use the value of \(f(3)\) as the new input for \(g(x)\).
- Follow the horizontal line to the line representing \(y = g(x)\).
- Read the y-coordinate to find the value of \(g(f(3))\).
Fill in the evaluated values in the respective input boxes.
---
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
