College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.4: Operations On Functions
Problem 124E
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Question
![### Function Composition Evaluation
Suppose that the functions \( u \) and \( w \) are defined as follows:
\[ u(x) = \frac{x^2 + 9}{9} \]
\[ w(x) = \sqrt{x + 8} \]
Find the following compositions:
\[
\left( w \circ u \right) (8) = \quad \boxed{}
\]
\[
\left( u \circ w \right) (8) = \quad \boxed{}
\]
### Steps for Solving Composition of Functions
1. **Finding \( ( w \circ u )(8) \)**
- First, evaluate \( u(8) \).
- Then, use the result from \( u(8) \) as the input for \( w \).
2. **Finding \( ( u \circ w )(8) \)**
- First, evaluate \( w(8) \).
- Then, use the result from \( w(8) \) as the input for \( u \).
### Interactive Section
The image includes an interactive component where students can input their answers. The controls include options to check the answers (\( \square_{--}^{--}\)), reset the inputs (\( \rotate \)), and get hints or guidance (\( ? \)).
### User Navigation
At the bottom, there is a "Continue" button for progressing to the next part of the activity or lesson once the students have input their answers and are ready to move forward.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39e42e2d-e50a-4730-a160-ebeade812b32%2Fb4c26119-3dbf-44ed-b3bf-2a0cd664fe25%2F8l2v30g_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Function Composition Evaluation
Suppose that the functions \( u \) and \( w \) are defined as follows:
\[ u(x) = \frac{x^2 + 9}{9} \]
\[ w(x) = \sqrt{x + 8} \]
Find the following compositions:
\[
\left( w \circ u \right) (8) = \quad \boxed{}
\]
\[
\left( u \circ w \right) (8) = \quad \boxed{}
\]
### Steps for Solving Composition of Functions
1. **Finding \( ( w \circ u )(8) \)**
- First, evaluate \( u(8) \).
- Then, use the result from \( u(8) \) as the input for \( w \).
2. **Finding \( ( u \circ w )(8) \)**
- First, evaluate \( w(8) \).
- Then, use the result from \( w(8) \) as the input for \( u \).
### Interactive Section
The image includes an interactive component where students can input their answers. The controls include options to check the answers (\( \square_{--}^{--}\)), reset the inputs (\( \rotate \)), and get hints or guidance (\( ? \)).
### User Navigation
At the bottom, there is a "Continue" button for progressing to the next part of the activity or lesson once the students have input their answers and are ready to move forward.
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