Let's solve the given expressions using the table of values provided in the image.

Table Recap:

• $f(x)$ and $g(x)$ are functions, and the values of these functions for various inputs $x$ are given in the table.
  • For example:
    • $f(0) = 2$, $g(0) = 7$
    • $f(1) = 5$, $g(1) = 9$
    • $f(2) = 4$, $g(2) = 0$, etc.

1. $f(g(9))$

• First, find $g(9)$ from the table:
  • $g(9) = 8$
• Now, find $f(8)$:
  • $f(8) = 6$
• Therefore, $f(g(9)) = 6$.

2. $g(f(7))$

• First, find $f(7)$ from the table:
  • $f(7) = 1$
• Now, find $g(1)$:
  • $g(1) = 9$
• Therefore, $g(f(7)) = 9$.

3. $f(f(2))$

• First, find $f(2)$ from the table:
  • $f(2) = 4$
• Now, find $f(4)$:
  • $f(4) = 9$
• Therefore, $f(f(2)) = 9$.

4. $g(g(6))$

• First, find $g(6)$ from the table:
  • $g(6) = 4$
• Now, find $g(4)$:
  • $g(4) = 2$
• Therefore, $g(g(6)) = 2$.

Final Answers:

1. $f(g(9)) = 6$
2. $g(f(7)) = 9$
3. $f(f(2)) = 9$
4. $g(g(6)) = 2$

Would you like further details or explanations on any step?

Here are 5 related questions:

1. What is $f(f(3))$?
2. Can you find $g(f(4))$?
3. What is $f(g(0))$?
4. What is the value of $g(g(3))$?
5. Can you solve for $f(g(5))$?

Tip: In function compositions, always solve from the innermost function first!