The problem asks us to evaluate composite functions using a table of values for functions $f(x)$ and $g(x)$. We need to find $f(g(2))$, $g(f(7))$, $f(f(8))$, and $g(g(5))$.

1. Problem Description

The problem asks us to evaluate composite functions using a table of values for functions $f(x)$ and $g(x)$. We need to find $f(g(2))$, $g(f(7))$, $f(f(8))$, and $g(g(5))$.

2. Solution Steps

a) Evaluate $f(g(2))$:

From the table, we find $g(2) = 1$.

Then, we need to evaluate $f(1)$. From the table, $f(1) = 1$.

Therefore, $f(g(2)) = f(1) = 1$.

b) Evaluate $g(f(7))$:

From the table, we find $f(7) = 8$.

Then, we need to evaluate $g(8)$. From the table, $g(8) = 7$.

Therefore, $g(f(7)) = g(8) = 7$.

c) Evaluate $f(f(8))$:

From the table, we find $f(8) = 0$.

Then, we need to evaluate $f(0)$. From the table, $f(0) = 9$.

Therefore, $f(f(8)) = f(0) = 9$.

d) Evaluate $g(g(5))$:

From the table, we find $g(5) = 5$.

Then, we need to evaluate $g(5)$. From the table, $g(5) = 5$.

Therefore, $g(g(5)) = g(5) = 5$.

3. Final Answer

$f(g(2)) = 1$

$g(f(7)) = 7$

$f(f(8)) = 9$

$g(g(5)) = 5$