To solve for $f(g(3))$, we need to break this down step by step using the tables provided.

Step 1: Find $g(3)$

Looking at the second table, which defines the values of $g(x)$:

• For $x = 3$, $g(3) = 5$.

Step 2: Find $f(g(3)) = f(5)$

Now that we know $g(3) = 5$, we can substitute this into $f$. Referring to the first table, which defines $f(x)$:

• For $x = 5$, $f(5) = 4$.

Thus, the value of $f(g(3))$ is 4.

Would you like more details or have any other questions?

Follow-up Questions:

1. What is the value of $f(g(2))$?
2. What is $g(f(4))$?
3. How do you solve nested function problems in general?
4. If $f(x)$ were changed, how would that affect $f(g(3))$?
5. What is the significance of the order of function composition?

Tip: When dealing with nested functions like $f(g(x))$, always start from the innermost function and work outward.