To evaluate the function addition \( (f + g)(x) \) at \( x = -1 \), we'll first add the functions \( f(x) \) and \( g(x) \), then substitute \( x = -1 \) into the resulting expression.

### Step 1: Add the functions
\[ (f + g)(x) = f(x) + g(x) \]
Given:
\[ f(x) = 2x^3 - 2x^2 \]
\[ g(x) = x^3 - 4 \]

Adding these:
\[
(f + g)(x) = (2x^3 - 2x^2) + (x^3 - 4)
\]
Combine like terms:
\[
(f + g)(x) = 3x^3 - 2x^2 - 4
\]

### Step 2: Evaluate at \( x = -1 \)
Substitute \( x = -1 \) into the expression:
\[
(f + g)(-1) = 3(-1)^3 - 2(-1)^2 - 4
\]

Calculate each term:
\[
(-1)^3 = -1, \quad (-1)^2 = 1
\]
\[
(f + g)(-1) = 3(-1) - 2(1) - 4 = -3 - 2 - 4 = -9
\]

So, \( (f + g)(-1) = -9 \).

Would you like more details or have any questions?

Here are some related questions:
1. What is \( (f + g)(1) \)?
2. What is \( (f - g)(-1) \)?
3. What is \( f(-1) \)?
4. What is \( g(-1) \)?
5. How do you perform function multiplication \( (f \cdot g)(x) \) at \( x = -1 \)?
6. What is the derivative of \( (f + g)(x) \)?
7. What is the integral of \( (f + g)(x) \)?
8. How would you solve \( (f + g)(x) = 0 \)?

**Tip:** When evaluating a function, always substitute carefully and simplify step by step to avoid mistakes!

Learn how to evaluate the function addition (f + g)(x) at x = -1 with a detailed step-by-step solution. This problem covers adding functions, substituting values, and simplifying algebraic expressions. Suitable for high school students.

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