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The problem asks for the value of \( g(-2) \), given the composite function \( g \circ f(x) = \frac{3x - 5}{2x - 2} \), with the condition \( x \neq 1 \), and the function \( f(x) = 3x - 1 \).

### Step-by-Step Solution

1. **Understanding the composite function**:
   - The composite function is given by:
     \[
     g(f(x)) = \frac{3x - 5}{2x - 2}
     \]
     This means that \( g(f(x)) = \frac{3x - 5}{2x - 2} \).

2. **Substitute the expression for \( f(x) \) into the composite function**:
   - We are given that \( f(x) = 3x - 1 \).
   - To find \( g(x) \), let's assume the composite \( g(f(x)) = \frac{3x - 5}{2x - 2} \) means we replace \( f(x) \) into this equation. We already know \( f(x) = 3x - 1 \).

3. **Find \( g(y) \) by substituting \( y = f(x) = 3x - 1 \)**:
   - Let \( y = f(x) = 3x - 1 \), then \( x = \frac{y + 1}{3} \).
   - Substitute this into the composite function:
     \[
     g(y) = \frac{3\left( \frac{y + 1}{3} \right) - 5}{2\left( \frac{y + 1}{3} \right) - 2}
     \]
     Simplifying both the numerator and the denominator:
     - Numerator:
       \[
       3\left( \frac{y + 1}{3} \right) - 5 = y + 1 - 5 = y - 4
       \]
     - Denominator:
       \[
       2\left( \frac{y + 1}{3} \right) - 2 = \frac{2(y + 1)}{3} - 2 = \frac{2y + 2}{3} - \frac{6}{3} = \frac{2y + 2 - 6}{3} = \frac{2y - 4}{3}
       \]
     Now we have:
     \[
     g(y) = \frac{y - 4}{\frac{2y - 4}{3}} = \frac{3(y - 4)}{2y - 4}
     \]
     Factor the denominator:
     \[
     g(y) = \frac{3(y - 4)}{2(y - 2)}
     \]

4. **Find \( g(-2) \)**:
   - Substitute \( y = -2 \) into the equation for \( g(y) \):
     \[
     g(-2) = \frac{3(-2 - 4)}{2(-2 - 2)} = \frac{3(-6)}{2(-4)} = \frac{-18}{-8} = \frac{9}{4}
     \]

### Final Answer:
\[
g(-2) = \frac{9}{4}
\]

Would you like any further clarification on these steps?

Here are some related questions you might consider:
1. How do we handle composite functions in other contexts?
2. What are the general steps for solving \( g(f(x)) \) problems?
3. How do we factor expressions to simplify fractions?
4. How do restrictions on domain affect the function?
5. What happens when the denominator of a function becomes zero?

**Tip:** Always check for any domain restrictions, especially when dealing with rational functions.

Diketahui g∘f(x)= (3x−5)/(2x−2) , x ≠ 1 dan f(x) = 3x − 1, maka nilai g(−2) = ....

Learn how to calculate g(-2) from the composite function g∘f(x) = (3x−5)/(2x−2) and f(x) = 3x − 1. This step-by-step guide covers composite functions, substitution, and domain restrictions. Suitable for high school students in Grades 10-12.

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