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The problem in your image asks to determine if the function \( f(x) = 5x^2 + 3x^2 - 2 \) is even, odd, or neither.

To solve this:

1. **Step 1: Check if the function is even**
   - A function is **even** if \( f(-x) = f(x) \) for all \( x \).
   - Let’s substitute \( -x \) into the function:
     \[
     f(-x) = 5(-x)^2 + 3(-x)^2 - 2 = 5x^2 + 3x^2 - 2
     \]
   - Since \( f(-x) = f(x) \), the function is **even**.

2. **Conclusion**: The function is **even**.

Would you like more details or have any further questions on this? Here are some related questions you could explore:

1. What is the formal definition of an odd function?
2. How can you determine if a function is neither even nor odd?
3. Are there any functions that can be both even and odd?
4. What role do powers of \( x \) play in determining if a function is even or odd?
5. How does symmetry relate to even and odd functions?

**Tip:** For polynomial functions, even powers of \( x \) indicate even behavior, while odd powers indicate odd behavior.

Determine if the following function is even, odd, or neither. f(x) = 5x^2 + 3x^2 - 2

Learn how to determine if the function f(x) = 5x^2 + 3x^2 - 2 is even, odd, or neither. This problem covers key concepts such as polynomial functions and even/odd function properties. Suitable for students in Grades 10-12.

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