Let's tackle this problem step-by-step.
1. Identify \( g(2) \):
- We need to find the value of the function \( g \) at \( x = 2 \).
- According to the table, \( g(2) = 2 \).
2. Find \( f^{-1}(g(2)) \):
- Now, we need to determine the value of \( f^{-1}(y) \) where \( y = g(2) \). This means we need to find \( x \) such that \( f(x) = 2 \).
3. Look up \( f(x) = 2 \) in the table:
- From the table, the value of \( f(x) = 2 \) occurs when \( x = 4 \).
Therefore, \( f^{-1}(g(2)) = 4 \).
So the detailed steps give us the final result:
[tex]\[ f^{-1}(g(2)) = 4 \][/tex]
