9. Find composition fog for pairs of real functions f, g. (a) f(a) = 3r + 1, 9(a) = a2 + 1 (b) f(x) = r(x - 2), g(x) = (r+ 1)/4 %3D
9. Find composition fog for pairs of real functions f, g. (a) f(a) = 3r + 1, 9(a) = a2 + 1 (b) f(x) = r(x - 2), g(x) = (r+ 1)/4 %3D
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
![**Problem 9: Composition of Functions**
Find the composition \( f \circ g \) for the given pairs of real functions \( f \) and \( g \).
**(a)**
- \( f(x) = 3x + 1 \)
- \( g(x) = x^2 + 1 \)
**(b)**
- \( f(x) = x(x - 2) \)
- \( g(x) = (x + 1)/4 \)
**Instructions:**
To find the composition \( f \circ g \), substitute the expression for \( g(x) \) into the function \( f(x) \).
**Example Calculation:**
For part (a), compute \( f(g(x)) \) as follows:
1. Identify \( g(x) = x^2 + 1 \).
2. Substitute \( x^2 + 1 \) into \( f(x)\):
\[
f(g(x)) = f(x^2 + 1) = 3(x^2 + 1) + 1 = 3x^2 + 3 + 1 = 3x^2 + 4
\]
Perform similar steps for part (b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f2e78f4-02a6-4843-ac83-b4141c1bc59d%2Fec5dc980-070a-4995-bb53-8541a71ee68d%2F5pydzh3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 9: Composition of Functions**
Find the composition \( f \circ g \) for the given pairs of real functions \( f \) and \( g \).
**(a)**
- \( f(x) = 3x + 1 \)
- \( g(x) = x^2 + 1 \)
**(b)**
- \( f(x) = x(x - 2) \)
- \( g(x) = (x + 1)/4 \)
**Instructions:**
To find the composition \( f \circ g \), substitute the expression for \( g(x) \) into the function \( f(x) \).
**Example Calculation:**
For part (a), compute \( f(g(x)) \) as follows:
1. Identify \( g(x) = x^2 + 1 \).
2. Substitute \( x^2 + 1 \) into \( f(x)\):
\[
f(g(x)) = f(x^2 + 1) = 3(x^2 + 1) + 1 = 3x^2 + 3 + 1 = 3x^2 + 4
\]
Perform similar steps for part (b).
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
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,
