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Let's analyze the problem step by step.

We are given two functions:
- \( f(x) = 3x - 2 \)
- \( (g \circ f)(x) = 9x^2 - 7 \), which means \( g(f(x)) = 9x^2 - 7 \)

We need to find the formula for \( g(x) \).

### Step-by-Step Solution:

1. First, substitute \( f(x) = 3x - 2 \) into the composition \( g(f(x)) \):
   \[
   g(3x - 2) = 9x^2 - 7
   \]

2. To find \( g(x) \), let's set \( u = 3x - 2 \), so the equation becomes:
   \[
   g(u) = 9x^2 - 7
   \]

3. Solve for \( x \) in terms of \( u \):
   \[
   u = 3x - 2 \quad \Rightarrow \quad 3x = u + 2 \quad \Rightarrow \quad x = \frac{u + 2}{3}
   \]

4. Now substitute \( x = \frac{u + 2}{3} \) back into \( 9x^2 - 7 \):
   \[
   9x^2 = 9\left(\frac{u + 2}{3}\right)^2 = 9 \times \frac{(u + 2)^2}{9} = (u + 2)^2
   \]
   So:
   \[
   g(u) = (u + 2)^2 - 7
   \]
   Expand \( (u + 2)^2 \):
   \[
   g(u) = u^2 + 4u + 4 - 7 = u^2 + 4u - 3
   \]

5. Therefore, the function \( g(x) \) is:
   \[
   g(x) = x^2 + 4x - 3
   \]

The correct answer is **Option D**.

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Would you like any more details or explanations?

Here are some related questions for further practice:
1. If \( f(x) = 2x + 1 \) and \( g(f(x)) = 4x^2 + 5x \), find \( g(x) \).
2. How would you verify if \( g(x) = x^2 + 4x - 3 \) is correct for all \( x \)?
3. How do we derive the inverse of \( f(x) = 3x - 2 \)?
4. If \( (g \circ h)(x) = 25x^2 - 16 \), and \( h(x) = 5x + 4 \), find \( g(x) \).
5. What is the domain and range of the function \( g(x) = x^2 + 4x - 3 \)?

**Tip:** When working with function compositions, always substitute the given functions carefully and check for algebraic simplifications.

Jika f(x) = 3x - 2, x ∈ R, dan (g ∘ f)(x) = 9x² - 7, x ∈ R. Rumus fungsi g(x) = ...

Learn how to find the formula for g(x) given f(x) = 3x - 2 and the composition (g ∘ f)(x) = 9x² - 7. This step-by-step solution involves key algebraic concepts such as function composition, substitution methods, and quadratic equations. Suitable for high school students in Grades 10-12.

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