https://file.aiquickdraw.com/mathbot/file/1727004822004biiuuomz.jpg

The image provides the following mathematical functions and tasks:

Given:
- \( f(x) = x^2 - 4 \)
- \( g(x) = 3x + 5 \)
- \( h(x) = 2 - 2x \)

Find:
1. \( (f \circ g)(2) \)
2. \( (g \circ h)(4) \)
3. \( (g \circ f)(2) \)

Let's solve each:

### 1. \( (f \circ g)(2) \)
This represents \( f(g(2)) \):
- First, calculate \( g(2) \):  
  \( g(2) = 3(2) + 5 = 6 + 5 = 11 \)
- Then, calculate \( f(11) \):  
  \( f(11) = 11^2 - 4 = 121 - 4 = 117 \)

Thus, \( (f \circ g)(2) = 117 \).

### 2. \( (g \circ h)(4) \)
This represents \( g(h(4)) \):
- First, calculate \( h(4) \):  
  \( h(4) = 2 - 2(4) = 2 - 8 = -6 \)
- Then, calculate \( g(-6) \):  
  \( g(-6) = 3(-6) + 5 = -18 + 5 = -13 \)

Thus, \( (g \circ h)(4) = -13 \).

### 3. \( (g \circ f)(2) \)
This represents \( g(f(2)) \):
- First, calculate \( f(2) \):  
  \( f(2) = 2^2 - 4 = 4 - 4 = 0 \)
- Then, calculate \( g(0) \):  
  \( g(0) = 3(0) + 5 = 0 + 5 = 5 \)

Thus, \( (g \circ f)(2) = 5 \).

### Final Answers:
1. \( (f \circ g)(2) = 117 \)
2. \( (g \circ h)(4) = -13 \)
3. \( (g \circ f)(2) = 5 \)

Let me know if you'd like further clarification on any of these steps!

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Here are 5 related questions to expand your understanding:
1. What is \( (f \circ h)(3) \)?
2. How would you calculate \( (h \circ f)(-1) \)?
3. What is the inverse of \( f(x) = x^2 - 4 \) for positive \( x \)?
4. How would you find \( (g \circ g)(2) \)?
5. How does the composition of functions change if you swap the order, as in \( (f \circ g) \) versus \( (g \circ f) \)?

### Tip:
When composing functions, always calculate from the inside out, starting with the innermost function and working outward.

Diketahui f(x) = x^2 - 4, g(x) = 3x + 5, dan h(x) = 2 - 2x. Tentukan: 1. (f o g)(2), 2. (g o h)(4), 3. (g o f)(2).

Learn how to solve function composition problems involving f(x) = x^2 - 4, g(x) = 3x + 5, and h(x) = 2 - 2x. We will determine (f o g)(2), (g o h)(4), and (g o f)(2) step by step. Suitable for students in Grades 10-12.

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