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The problem asks to determine the function \( g(x) \) given that:

1. \( (f \circ g)(x) = 2x + 5 \) and \( f(x) = x + 6 \)
2. \( (f \circ g)(x) = 1 - 4x \) and \( f(x) = 2x + 13 \)

The composition of functions \( (f \circ g)(x) \) means that \( f(g(x)) \) should equal the given expression for each case. Let's solve for \( g(x) \) in both cases.

---

### 1. Case a
Given:
\[
(f \circ g)(x) = 2x + 5 \quad \text{and} \quad f(x) = x + 6
\]

1. Substitute \( g(x) \) into \( f(x) \) so that \( f(g(x)) = 2x + 5 \).
   Since \( f(x) = x + 6 \), replace \( x \) with \( g(x) \):
   \[
   f(g(x)) = g(x) + 6
   \]

2. Set up the equation:
   \[
   g(x) + 6 = 2x + 5
   \]

3. Solve for \( g(x) \):
   \[
   g(x) = 2x + 5 - 6
   \]
   \[
   g(x) = 2x - 1
   \]

So, for part (a), \( g(x) = 2x - 1 \).

---

### 2. Case b
Given:
\[
(f \circ g)(x) = 1 - 4x \quad \text{and} \quad f(x) = 2x + 13
\]

1. Substitute \( g(x) \) into \( f(x) \) so that \( f(g(x)) = 1 - 4x \).
   Since \( f(x) = 2x + 13 \), replace \( x \) with \( g(x) \):
   \[
   f(g(x)) = 2g(x) + 13
   \]

2. Set up the equation:
   \[
   2g(x) + 13 = 1 - 4x
   \]

3. Solve for \( g(x) \):
   \[
   2g(x) = 1 - 4x - 13
   \]
   \[
   2g(x) = -4x - 12
   \]
   \[
   g(x) = -2x - 6
   \]

So, for part (b), \( g(x) = -2x - 6 \).

---

### Summary
- For part (a), \( g(x) = 2x - 1 \).
- For part (b), \( g(x) = -2x - 6 \).

Would you like a more detailed explanation of any of these steps? 

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Here are some related questions you might find useful to explore:

1. How does function composition work in general?
2. What if \( f(x) \) or \( g(x) \) were nonlinear functions—how would that affect the solution?
3. How can we check if our solution for \( g(x) \) is correct?
4. What are the properties of composite functions?
5. Can we have multiple solutions for \( g(x) \) in this type of problem?

**Tip:** When dealing with function compositions, rewriting \( f(g(x)) \) explicitly in terms of \( g(x) \) can often make the problem clearer and easier to solve.

Tentukan fungsi g(x) jika diketahui (f o g)(x) = 2x + 5 dan f(x) = x + 6, serta (f o g)(x) = 1 - 4x dan f(x) = 2x + 13

Learn how to find the function g(x) from the composition of functions (f o g)(x) = 2x + 5, f(x) = x + 6, and similar function compositions. This problem involves algebra and function composition, suitable for students in Grades 10-12.

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