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Let's solve each of the composite function problems using the provided tables.

### Given Functions:
- \( f(x) = x^2 - 15 \)
- \( g(x) = \sqrt{x} \)

### For each question:

**19) \( (f \circ g)(36) \)**
This means \( f(g(36)) \).

- First, find \( g(36) \) from the table: \( g(36) = 6 \).
- Now, find \( f(6) \) from the table: \( f(6) = 21 \).

Thus, \( (f \circ g)(36) = 21 \).

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**20) \( (g \circ g)(16) \)**
This means \( g(g(16)) \).

- First, find \( g(16) \) from the table: \( g(16) = 4 \).
- Now, find \( g(4) \) from the table: \( g(4) = 2 \).

Thus, \( (g \circ g)(16) = 2 \).

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**21) \( (g \circ f)(4) \)**
This means \( g(f(4)) \).

- First, find \( f(4) \) from the table: \( f(4) = 1 \).
- Now, find \( g(1) \) from the table: \( g(1) = 1 \).

Thus, \( (g \circ f)(4) = 1 \).

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**22) \( (f \circ f)(4) \)**
This means \( f(f(4)) \).

- First, find \( f(4) \) from the table: \( f(4) = 1 \).
- Now, find \( f(1) \) from the table: \( f(1) = -14 \).

Thus, \( (f \circ f)(4) = -14 \).

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Would you like further clarification or details on any of these solutions?

Here are 5 related questions to consider:
1. What is \( (f \circ g)(25) \)?
2. What is \( (g \circ f)(7) \)?
3. What is the result of \( f(g(49)) \)?
4. How would you compute \( g(g(36)) \)?
5. What is \( f(f(7)) \)?

**Tip:** When working with composite functions, always start from the innermost function and work your way out step by step.

Use the tables of ordered pairs to determine the value of each composite function (f ∘ g)(36), (g ∘ g)(16), (g ∘ f)(4), and (f ∘ f)(4).

Learn how to solve composite functions such as (f ∘ g)(36), (g ∘ g)(16), and more using function tables for f(x) = x^2 - 15 and g(x) = √x. This detailed solution is suitable for students in Grades 9-11.

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