https://file.aiquickdraw.com/mathbot/file/1726152616768ldvw3352.jpg

The image shows a math problem asking to evaluate two composite functions using the given functions:

1. \( f(x) = x - 5 \)
2. \( g(x) = x + 5 \)

The questions are:

1. What is \( f(g(11)) \)?
2. What is \( g(f(11)) \)?

### Solution:

#### 1. Evaluating \( f(g(11)) \):

First, find \( g(11) \):

\[
g(11) = 11 + 5 = 16
\]

Now, substitute \( g(11) \) into \( f(x) \):

\[
f(g(11)) = f(16) = 16 - 5 = 11
\]

So, \( f(g(11)) = 11 \).

#### 2. Evaluating \( g(f(11)) \):

First, find \( f(11) \):

\[
f(11) = 11 - 5 = 6
\]

Now, substitute \( f(11) \) into \( g(x) \):

\[
g(f(11)) = g(6) = 6 + 5 = 11
\]

So, \( g(f(11)) = 11 \).

### Final Answers:

1. \( f(g(11)) = 11 \)
2. \( g(f(11)) = 11 \)

Would you like further details or have any questions?

### Related Questions:

1. How do you find the inverse of a function?
2. What is the difference between composite functions and inverse functions?
3. How do you evaluate composite functions for more complex expressions?
4. What are some practical applications of composite functions?
5. How can you graph composite functions?

#### Tip: 
When evaluating composite functions, always work from the inside out, starting with the innermost function first.

Given the functions f(x) = x - 5 and g(x) = x + 5, evaluate the composite functions: 1. What is f(g(11))? 2. What is g(f(11))?

Learn how to evaluate composite functions f(g(11)) and g(f(11)) step by step. Using the functions f(x) = x - 5 and g(x) = x + 5, this problem is designed for students in Grades 9-10. A detailed solution for each composite function is provided.

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