### Function Composition EvaluationSuppose 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 Functions1. **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 $.### Interactive SectionThe image includes an interactive component where students can input their answers. The controls include options to check the answers ($ \square_{--}^{--}$), reset the inputs ($ \rotate $), and get hints or guidance ($ ? $).### User NavigationAt 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.

Name: ### Function Composition EvaluationSuppose that the functions $ u $
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Description: ### Function Composition EvaluationSuppose 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(

Given :u(x)=x2+9w(x)=x+8To determine,(wou)(8)(uow)(8)

Answered: u (x) =x²+9 w (x) = Vx+8 Find the…

Math

Algebra

u (x) =x²+9 w (x) = Vx+8 Find the following.

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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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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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.

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