Operation of function f(x) = 2x³-2x²  g(x) = x³-4

To find the operation between the functions \( f(x) = 2x^3 - 2x^2 \) and \( g(x) = x^3 - 4 \), you need to specify what operation you're interested in. Common operations include:

1. **Addition**: \( (f + g)(x) = f(x) + g(x) \)
2. **Subtraction**: \( (f - g)(x) = f(x) - g(x) \)
3. **Multiplication**: \( (f \cdot g)(x) = f(x) \cdot g(x) \)
4. **Division**: \( \left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)} \)
5. **Composition**: \( (f \circ g)(x) = f(g(x)) \) and \( (g \circ f)(x) = g(f(x)) \)

Let me know which operation you would like to perform!

Would you like more details or have any questions?

Here are some related questions:
1. What is the result of \( (f + g)(x) \)?
2. What is the result of \( (f - g)(x) \)?
3. What is the result of \( (f \cdot g)(x) \)?
4. What is the result of \( \left(\frac{f}{g}\right)(x) \)?
5. How do you perform the composition \( (f \circ g)(x) \)?
6. How do you perform the composition \( (g \circ f)(x) \)?
7. What are the roots of \( f(x) = 0 \)?
8. What are the roots of \( g(x) = 0 \)?

**Tip:** When performing function operations, always simplify the resulting expression if possible!

Explore operations between the functions f(x) = 2x³ - 2x² and g(x) = x³ - 4. Learn about addition, subtraction, multiplication, division, and composition of functions. Suitable for high school students studying advanced algebra.

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