Given the functions \( F(x) = x^3 + 2x^2 \) and \( g(x) = 3x^2 - 1 \), you can perform various operations or analyses. Here are a few possibilities:

1. **Find \( (F + g)(x) \):** The sum of the two functions.
2. **Find \( (F - g)(x) \):** The difference between the two functions.
3. **Find \( (F \cdot g)(x) \):** The product of the two functions.
4. **Find \( \frac{F}{g}(x) \):** The quotient of the two functions, assuming \( g(x) \neq 0 \).
5. **Find the composition \( F(g(x)) \) or \( g(F(x)) \):** Substitute one function into the other.

Would you like to explore any of these, or is there another operation or analysis you're interested in? 

Here are some related questions:

1. How do you find the derivative of \( F(x) \) and \( g(x) \)?
2. What are the roots of \( F(x) = 0 \) and \( g(x) = 0 \)?
3. How do you find the intersection points of \( F(x) \) and \( g(x) \)?
4. What is the area between the curves of \( F(x) \) and \( g(x) \)?
5. Can you find the limits \( \lim_{x \to c} F(x) \) and \( \lim_{x \to c} g(x) \) for a given value of \( c \)?

**Tip:** Understanding the composition of functions \( F(g(x)) \) and \( g(F(x)) \) can reveal more about how these functions interact with each other.

Discover how to analyze and operate with the functions F(x) = x^3 + 2x^2 and g(x) = 3x^2 - 1. Learn about sum, difference, product, and quotient of functions, along with compositions and other related operations. Suitable for high school students.

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