Define f (x) = 4+ x – x² and g(x) = 5x – 3. Define f(x) - - (f o g)(x) = (go f)(x). True False
Define f (x) = 4+ x – x² and g(x) = 5x – 3. Define f(x) - - (f o g)(x) = (go f)(x). True False
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![**Question: Functional Composition**
Define \( f(x) = 4 + x - x^2 \) and \( g(x) = 5x - 3 \).
Then \( (f \circ g)(x) = (g \circ f)(x) \).
- [ ] True
- [ ] False
**Explanation:**
In this problem, we are given two functions \( f(x) \) and \( g(x) \) and asked whether their compositions are equal regardless of the order of the composition.
Let’s compute each composition:
1. **For \( (f \circ g)(x) \):**
This means we substitute \( g(x) \) into \( f(x) \):
\[
(f \circ g)(x) = f(g(x)) = f(5x - 3)
\]
Plug \( 5x - 3 \) into \( f(x) \):
\[
f(5x - 3) = 4 + (5x - 3) - (5x - 3)^2
\]
2. **For \( (g \circ f)(x) \):**
This means we substitute \( f(x) \) into \( g(x) \):
\[
(g \circ f)(x) = g(f(x)) = g(4 + x - x^2)
\]
Plug \( 4 + x - x^2 \) into \( g(x) \):
\[
g(4 + x - x^2) = 5(4 + x - x^2) - 3
\]
After computing both compositions, compare them to check if they are equal. This involves both distribution and simplification.
**Answer the question by selecting either True or False based on your computations.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24861ef-92b0-4cd8-8c54-2ac2200498ec%2F0c252a54-b5a4-48de-8961-23d2be9ffd0f%2F3p5qygo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question: Functional Composition**
Define \( f(x) = 4 + x - x^2 \) and \( g(x) = 5x - 3 \).
Then \( (f \circ g)(x) = (g \circ f)(x) \).
- [ ] True
- [ ] False
**Explanation:**
In this problem, we are given two functions \( f(x) \) and \( g(x) \) and asked whether their compositions are equal regardless of the order of the composition.
Let’s compute each composition:
1. **For \( (f \circ g)(x) \):**
This means we substitute \( g(x) \) into \( f(x) \):
\[
(f \circ g)(x) = f(g(x)) = f(5x - 3)
\]
Plug \( 5x - 3 \) into \( f(x) \):
\[
f(5x - 3) = 4 + (5x - 3) - (5x - 3)^2
\]
2. **For \( (g \circ f)(x) \):**
This means we substitute \( f(x) \) into \( g(x) \):
\[
(g \circ f)(x) = g(f(x)) = g(4 + x - x^2)
\]
Plug \( 4 + x - x^2 \) into \( g(x) \):
\[
g(4 + x - x^2) = 5(4 + x - x^2) - 3
\]
After computing both compositions, compare them to check if they are equal. This involves both distribution and simplification.
**Answer the question by selecting either True or False based on your computations.**
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