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To solve this problem, we need to evaluate the combined function \((f \circ g)(-2)\) for the given functions \( f(x) = x^3 + x^2 \) and \( g(x) = x^3 - 4 \).

### Step-by-Step Solution
1. **Evaluate \( g(-2) \):**
   Substitute \( x = -2 \) into \( g(x) = x^3 - 4 \):
   \[
   g(-2) = (-2)^3 - 4 = -8 - 4 = -12
   \]
   So, \( g(-2) = -12 \).

2. **Evaluate \( f(g(-2)) = f(-12) \):**
   Now we need to substitute \( x = -12 \) into \( f(x) = x^3 + x^2 \):
   \[
   f(-12) = (-12)^3 + (-12)^2
   \]
   Calculate each term separately:
   - \( (-12)^3 = -1728 \)
   - \( (-12)^2 = 144 \)
   
   Therefore,
   \[
   f(-12) = -1728 + 144 = -1584
   \]

### Final Answer
\[
(f \circ g)(-2) = -1584
\]

Let me know if you'd like more details or have any questions!

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Here are five related questions for further practice:

1. How would you evaluate \((g \circ f)(-2)\) for the same functions?
2. What is \((f \circ g)(1)\) for the given functions?
3. How would you approach finding \((f \circ g)(0)\)?
4. If \( h(x) = x^2 + 3x \), how would you calculate \((f \circ h)(2)\)?
5. What does it mean for a function to be "one-to-one," and how does this apply to \(f(x)\) or \(g(x)\)?

**Tip:** When working with composition of functions, always start by evaluating the innermost function first, then substitute its result into the outer function.

Find \((f \circ g)(-2)\) for the following functions: \( f(x) = x^3 + x^2 \) and \( g(x) = x^3 - 4 \).

Learn how to solve \((f \circ g)(-2)\) for functions \( f(x) = x^3 + x^2 \) and \( g(x) = x^3 - 4 \). This problem involves function composition, polynomials, and exponent rules, suitable for Grades 10-12.

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