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The problem asks for the result of \( f(-x) \) for the given function \( f(x) = 2x^2 + 3x - 4 \).

To solve this:

1. **Start with the function**:  
   \( f(x) = 2x^2 + 3x - 4 \)

2. **Substitute \( -x \) for \( x \)** in the function:  
   \( f(-x) = 2(-x)^2 + 3(-x) - 4 \)

3. **Simplify each term**:
   - \( (-x)^2 = x^2 \), so \( 2(-x)^2 = 2x^2 \)
   - \( 3(-x) = -3x \)
   - The constant term, \( -4 \), remains the same.

Thus, \( f(-x) = 2x^2 - 3x - 4 \).

The correct answer is **a.  \( 2x^2 - 3x - 4 \)**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you determine whether a function is even, odd, or neither?
2. What is the significance of substituting \( -x \) into a function?
3. How do different powers of \( x \) affect the behavior of \( f(-x) \)?
4. Can you graph the function \( f(x) = 2x^2 + 3x - 4 \) and its reflection \( f(-x) \)?
5. How would the answer change if the function had a different form, like \( f(x) = x^3 + x \)?

**Tip**: A function is **even** if \( f(-x) = f(x) \) for all \( x \), and **odd** if \( f(-x) = -f(x) \).

Dada la función f(x) = 2x^2 + 3x - 4, para f(-x) obtenemos:

Learn how to find f(-x) for the function f(x) = 2x^2 + 3x - 4 by substituting -x into the function and simplifying. This problem involves key algebraic concepts, suitable for Grades 9-12.

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