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The question is asking for the value of \((f \circ g)'(-1)\), where \( f(x) = 3x^2 - 2 \). To solve this, we need to determine the function \( g(x) \) and then find the composition \( f(g(x)) \), followed by differentiating the composite function and evaluating it at \( x = -1 \).

However, the function \( g(x) \) is not provided directly in the problem statement, so let's assume \( g(x) = x \), making the problem focus on evaluating \( f'(x) \) at \( x = -1 \).

### Step-by-Step Solution:
1. **Given Function**: \( f(x) = 3x^2 - 2 \).
2. **Differentiate \( f(x) \)**: 
   \[
   f'(x) = \frac{d}{dx}(3x^2 - 2) = 6x.
   \]
3. **Evaluate the Derivative at \( x = -1 \)**:
   \[
   f'(-1) = 6(-1) = -6.
   \]

Since \( g(x) \) was not explicitly given and was assumed to be \( x \), the calculated result would be different if \( g(x) \) was different. But based on our steps:

The final value is:

\[
f'(g(-1)) = f'(-1) = -6.
\]

However, since the available answer choices do not include this value, it suggests \( g(x) \) needs more information or a distinct interpretation might be necessary.

Would you like further clarification, or do you have any additional questions?

**Related Questions**:
1. How would the answer change if \( g(x) \) is given as a specific function, like \( g(x) = x^3 - x \)?
2. What are the principles behind chain rule applications in composite functions?
3. How does differentiating composite functions compare to differentiating simple functions?
4. What methods exist to check derivatives quickly?
5. Why is it crucial to know the inner function for correct chain rule application?

**Tip**: Always ensure clarity on the functions involved when dealing with compositions to avoid missteps in differentiation.

If f(x) = 3x^2 - 2, then (f ∘ g)'(-1) = ?

This problem focuses on function composition and differentiation using the chain rule. Learn how to evaluate (f ∘ g)'(-1), where f(x) = 3x^2 - 2, with detailed steps on applying the derivative and the chain rule. Suitable for Grades 10-12.

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