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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.

Values for the functions f and g are given in the tables above. What is the value of f(g(3))?

Learn how to solve a function composition problem involving two functions f and g, where f(g(3)) is calculated step by step using provided tables. Suitable for students in Grades 8-10, this problem covers key concepts of function composition.

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