### Lesson 6.3: Composition of Functions#### Find the composition of functions, if it exists.Given:- Function \( f \): \[ f = \{(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)\} \]- Function \( g \): \[ g = \{(-1, -3), (0, 2), (1, 4), (2, 5), (3, 7)\} \]- Function \( h \): \[ h = \{(-3, -5), (-1, -1), (1, 1), (3, 5)\} \]Exercises:1. \( 107. \ (f \circ g)(x) \)2. \( 108. \ (g \circ h)(x) \)3. \( 109. \ (f \circ h)(x) \)#### Explanation:**Composition of Functions:**- The composition of two functions \( f \) and \( g \), denoted \( (f \circ g)(x) \), is defined as \( f(g(x)) \). This means you first apply \( g \) to \( x \), then apply \( f \) to the result of \( g(x) \).**Detailed Steps to Solve Compositions:**1. **Composition \( (f \circ g)(x) \)**: - Identify the values of \( g(x) \) for each element in the domain of \( g \). - Use the output from \( g(x) \) as the input for \( f \) to find \( f(g(x)) \).2. **Composition \( (g \circ h)(x) \)**: - Identify the values of \( h(x) \) for each element in the domain of \( h \). - Use the output from \( h(x) \) as the input for \( g \) to find \( g(h(x)) \).3. **Composition \( (f \circ h)(x) \)**: - Identify the values of \( h(x) \) for each element in the domain of \( h \). - Use the output from \( h(x) \) as the input for \( f \) to find \(

We have to find the compositions of the given functions.

Lesson 6.3 Composition of Functions Find the composition of functions, if it exists. f={(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)} g= {(-1, -3), (0, 2), (1, 4), (2, 5), (3, 7)) h = {(-3,-5), (-1, -1), (1, 1), (3,5)} 107. (fog)(x) 108. (goh)(x) 109. (f h)(x)

Lesson 6.3 Composition of Functions Find the composition of functions, if it exists. f={(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)} g= {(-1, -3), (0, 2), (1, 4), (2, 5), (3, 7)) h = {(-3,-5), (-1, -1), (1, 1), (3,5)} 107. (fog)(x) 108. (goh)(x) 109. (f h)(x)

Intermediate Algebra

10th Edition

ISBN:9781285195728

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Functions

Section9.CR: Review Problem Set

Problem 24CR: An outpatient operating room charges each patient a fixed amount per surgery plus an amount per...

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Question

### Lesson 6.3: Composition of Functions

#### Find the composition of functions, if it exists.

Given:
- Function \( f \):
\[
f = \{(-4, 1), (-2, 4), (0, 5), (2, 6), (4, 8)\}
\]
- Function \( g \):
\[
g = \{(-1, -3), (0, 2), (1, 4), (2, 5), (3, 7)\}
\]
- Function \( h \):
\[
h = \{(-3, -5), (-1, -1), (1, 1), (3, 5)\}
\]

Exercises:
1. \( 107. \ (f \circ g)(x) \)
2. \( 108. \ (g \circ h)(x) \)
3. \( 109. \ (f \circ h)(x) \)

#### Explanation:

**Composition of Functions:**

- The composition of two functions \( f \) and \( g \), denoted \( (f \circ g)(x) \), is defined as \( f(g(x)) \). This means you first apply \( g \) to \( x \), then apply \( f \) to the result of \( g(x) \).

**Detailed Steps to Solve Compositions:**

1. **Composition \( (f \circ g)(x) \)**:
- Identify the values of \( g(x) \) for each element in the domain of \( g \).
- Use the output from \( g(x) \) as the input for \( f \) to find \( f(g(x)) \).

2. **Composition \( (g \circ h)(x) \)**:
- Identify the values of \( h(x) \) for each element in the domain of \( h \).
- Use the output from \( h(x) \) as the input for \( g \) to find \( g(h(x)) \).

3. **Composition \( (f \circ h)(x) \)**:
- Identify the values of \( h(x) \) for each element in the domain of \( h \).
- Use the output from \( h(x) \) as the input for \( f \) to find \(

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