https://file.aiquickdraw.com/mathbot/file/1728597083480xyea237i.jpg

Let's evaluate the given expressions using the table of values provided.

### 1. \( f(g(0)) \)
From the table:
- \( g(0) = 5 \)
Now, use this value to find \( f(5) \):
- \( f(5) = 1 \)

So, \( f(g(0)) = 1 \).

### 2. \( g(f(1)) \)
From the table:
- \( f(1) = 0 \)
Now, use this value to find \( g(0) \):
- \( g(0) = 5 \)

So, \( g(f(1)) = 5 \).

### 3. \( f(f(9)) \)
From the table:
- \( f(9) = 6 \)
Now, use this value to find \( f(6) \):
- \( f(6) = 9 \)

So, \( f(f(9)) = 9 \).

### 4. \( g(g(8)) \)
From the table:
- \( g(8) = 3 \)
Now, use this value to find \( g(3) \):
- \( g(3) = 6 \)

So, \( g(g(8)) = 6 \).

### Final Results:
- \( f(g(0)) = 1 \)
- \( g(f(1)) = 5 \)
- \( f(f(9)) = 9 \)
- \( g(g(8)) = 6 \)

Would you like more details or further explanations on any of these steps?

Here are some related questions to think about:
1. What would \( g(g(0)) \) be based on the table?
2. How do nested functions like \( f(f(x)) \) or \( g(g(x)) \) work conceptually?
3. Can you identify an input \( x \) where \( f(x) = g(x) \)?
4. What would the result be for \( f(g(9)) \)?
5. How can you describe the difference between \( f(x) \) and \( g(x) \) based on the values?

**Tip:** Always make sure to evaluate inner functions first when dealing with nested functions!

Use the table of values to evaluate the following expressions: f(g(0)), g(f(1)), f(f(9)), and g(g(8)).

Learn how to evaluate function compositions like f(g(0)), g(f(1)), f(f(9)), and g(g(8)) using a table of values. This problem demonstrates the key concepts of function evaluation and composition, ideal for Grades 9-11 students.

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