https://file.aiquickdraw.com/mathbot/file/17258586508904akv66qd.jpg

The image shows a table with values for \( f(x) \) and \( g(x) \), as well as some expressions to be filled in below the table. Let's extract the necessary data to help solve the expressions.

From the table, we have the following values for \( f(x) \) and \( g(x) \):

\[
\begin{array}{|c|c|c|}
\hline
x & f(x) & g(x) \\
\hline
0 & 8 & 7 \\
1 & 0 & 4 \\
2 & 4 & 5 \\
3 & 2 & 1 \\
4 & 5 & 9 \\
5 & 3 & 6 \\
6 & 1 & 8 \\
7 & 9 & 3 \\
9 & 7 & 4 \\
\hline
\end{array}
\]

The expressions to be filled are:

1. \( f(g(3)) \)
2. \( g(f(3)) = 4 \) (already filled in and correct)
3. \( f(f(5)) \)
4. \( g(g(1)) \)

### Let's solve them one by one:

1. **\( f(g(3)) \):**
   - First, find \( g(3) \). From the table, \( g(3) = 1 \).
   - Now, find \( f(1) \). From the table, \( f(1) = 0 \).
   - So, \( f(g(3)) = f(1) = 0 \).

2. **\( g(f(3)) = 4 \)** (already solved).

3. **\( f(f(5)) \):**
   - First, find \( f(5) \). From the table, \( f(5) = 3 \).
   - Now, find \( f(3) \). From the table, \( f(3) = 2 \).
   - So, \( f(f(5)) = f(3) = 2 \).

4. **\( g(g(1)) \):**
   - First, find \( g(1) \). From the table, \( g(1) = 4 \).
   - Now, find \( g(4) \). From the table, \( g(4) = 9 \).
   - So, \( g(g(1)) = g(4) = 9 \).

### Final answers:
1. \( f(g(3)) = 0 \)
3. \( f(f(5)) = 2 \)
4. \( g(g(1)) = 9 \)

Would you like more details or further explanations on any step?

Here are 5 related questions for further practice:
1. What is \( g(f(0)) \)?
2. What is \( f(g(6)) \)?
3. What is \( g(f(2)) \)?
4. What is \( f(f(4)) \)?
5. What is \( g(g(5)) \)?

**Tip:** When dealing with composite functions, always evaluate the innermost function first.

Given a table of values for f(x) and g(x), find f(g(3)), g(f(3)), f(f(5)), and g(g(1)).

Learn how to solve composite function expressions like f(g(3)), g(f(3)), f(f(5)), and g(g(1)) using a table of values. This exercise covers function composition and is suitable for students in Grades 8-10.

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