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The question provides two functions, \( f \) and \( g \), in the form of ordered pairs. You are asked to determine the values of compositions of these functions. Let's break it down step by step:

### Functions:
\[
f = \{(6, -2), (8, -1), (10, 0), (12, 1)\}
\]
\[
g = \{(-2, 8), (-1, 10), (0, 12), (1, 6)\}
\]

The compositions and evaluations requested are:
1. \( (f \circ g)(1) \)
2. \( (g \circ f)(6) \)
3. \( g \circ f \circ g \circ f(1) \)

### Step 1: \( (f \circ g)(1) \)
This means we need to find \( f(g(1)) \).
- From the set \( g \), \( g(1) = 6 \).
- Now we find \( f(6) \) from the set \( f \), which is \( f(6) = -2 \).

Thus, \( (f \circ g)(1) = -2 \).

### Step 2: \( (g \circ f)(6) \)
This means we need to find \( g(f(6)) \).
- From the set \( f \), \( f(6) = -2 \).
- Now we find \( g(-2) \) from the set \( g \), which is \( g(-2) = 8 \).

Thus, \( (g \circ f)(6) = 8 \).

### Step 3: \( g \circ f \circ g \circ f(1) \)
We need to evaluate this composition step by step:
- First, find \( f(1) \), but there is no pair in \( f \) for input \( 1 \), meaning this step fails.

Thus, the third composition cannot be evaluated since \( f(1) \) is undefined.

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Would you like a further breakdown or details on any of the steps? Here are five questions to consider:

1. What is the significance of function composition in mathematical operations?
2. How can function sets with undefined values impact calculations?
3. Can function compositions be applied to non-numeric domains, like strings or sets?
4. What are other methods for expressing functions besides ordered pairs?
5. How do these ordered pair mappings relate to real-world applications?

**Tip**: When performing function composition, always evaluate from the innermost function outward.

Diketahui fungsi f dan g yang dinyatakan dengan himpunan pasangan berurutan berikut: f = {(6, -2), (8, -1), (10, 0), (12, 1)} g = {(-2, 8), (-1, 10), (0, 12), (1, 6)} Tentukan f ∘ g, g ∘ f, (f ∘ g)(1), (g ∘ f)(6).

This problem involves calculating the composition of two functions, f and g, defined by sets of ordered pairs. It covers core algebraic concepts like function composition and ordered pair mappings, suitable for Grades 10-12.

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