Find f[g(x)] and g[f(x)] for the given functions. 10 f(x) = g(x)=x² X f[g(x)] =
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 Statement:**
Find \( f[g(x)] \) and \( g[f(x)] \) for the given functions.
**Functions:**
\( f(x) = \frac{10}{x} \)
\( g(x) = x^2 \)
**Tasks:**
- Calculate \( f[g(x)] \).
- Calculate \( g[f(x)] \).
To solve these, substitute the expression for one function into the other.
**1. Calculate \( f[g(x)] \):**
\[ f[g(x)] = f(x^2) \]
\[ f(x^2) = \frac{10}{x^2} \]
**2. Calculate \( g[f(x)] \):**
\[ g[f(x)] = g\left(\frac{10}{x}\right) \]
\[ g\left(\frac{10}{x}\right) = \left(\frac{10}{x}\right)^2 \]
\[ = \frac{100}{x^2} \]
**Conclusion:**
- \( f[g(x)] = \frac{10}{x^2} \)
- \( g[f(x)] = \frac{100}{x^2} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f191a8-a1b2-42ed-ac9e-32d60645d728%2Febd467ec-c185-4fb3-860b-8a30aae550b3%2F43wtzmd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find \( f[g(x)] \) and \( g[f(x)] \) for the given functions.
**Functions:**
\( f(x) = \frac{10}{x} \)
\( g(x) = x^2 \)
**Tasks:**
- Calculate \( f[g(x)] \).
- Calculate \( g[f(x)] \).
To solve these, substitute the expression for one function into the other.
**1. Calculate \( f[g(x)] \):**
\[ f[g(x)] = f(x^2) \]
\[ f(x^2) = \frac{10}{x^2} \]
**2. Calculate \( g[f(x)] \):**
\[ g[f(x)] = g\left(\frac{10}{x}\right) \]
\[ g\left(\frac{10}{x}\right) = \left(\frac{10}{x}\right)^2 \]
\[ = \frac{100}{x^2} \]
**Conclusion:**
- \( f[g(x)] = \frac{10}{x^2} \)
- \( g[f(x)] = \frac{100}{x^2} \)
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
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,
