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The question asks for the composition of two functions, \( g(f(x)) \), given the following:

- \( f(x) = 3x - 1 \)
- \( g(x) = x^2 - 2x - 5 \)

We are tasked with finding \( g(f(x)) \), meaning we substitute \( f(x) \) into \( g(x) \). 

### Step-by-step solution:

1. **Substitute \( f(x) = 3x - 1 \) into \( g(x) \)**:
   \[
   g(f(x)) = g(3x - 1)
   \]
   
2. **Now apply the function \( g(x) = x^2 - 2x - 5 \), replacing \( x \) with \( 3x - 1 \)**:
   \[
   g(3x - 1) = (3x - 1)^2 - 2(3x - 1) - 5
   \]

3. **Expand the squared term**:
   \[
   (3x - 1)^2 = (3x)^2 - 2(3x)(1) + (1)^2 = 9x^2 - 6x + 1
   \]

4. **Simplify the linear term**:
   \[
   -2(3x - 1) = -6x + 2
   \]

5. **Now substitute these into the original expression**:
   \[
   g(3x - 1) = 9x^2 - 6x + 1 - 6x + 2 - 5
   \]

6. **Simplify the expression**:
   \[
   g(3x - 1) = 9x^2 - 12x + (1 + 2 - 5) = 9x^2 - 12x - 2
   \]

Thus, \( g(f(x)) = 9x^2 - 12x - 2 \).

### Conclusion:
The correct answer is option **E**: \( 9x^2 - 12x - 2 \).

---

Do you need more details or have any questions? Here are 5 related questions to expand your understanding:

1. How would you compute \( f(g(x)) \) for the same functions?
2. Can you describe the general process of function composition?
3. How does expanding binomials help in solving function compositions?
4. What is the difference between \( g(f(x)) \) and \( f(g(x)) \)?
5. How would you solve this problem if one of the functions were a trigonometric function?

**Tip:** When composing functions, always substitute one function's result into the other carefully to avoid errors in simplification.

Diketahui f(x) = 3x - 1 dan g(x) = x^2 - 2x - 5. Fungsi komposisi (g o f)(x) = ...

This problem involves finding the composition of two functions, f(x) = 3x - 1 and g(x) = x^2 - 2x - 5. Learn how to solve it by applying function composition, binomial expansion, and algebraic simplification. Suitable for students in Grades 9-11.

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