Is the function `f(x)=x^(3n), n in N` even?

Explanation

To determine whether the function \( f(x) = x^{3n} \) (where \( n \) is a natural number) is even or odd, we need to analyze the function based on the definitions of even and odd functions.

### Step-by-step Solution:

1. **Understand the Definitions**:
- A function \( f(x) \) is **even** if \( f(-x) = f(x) \) for all \( x \).
- A function \( f(x) \) is **odd** if \( f(-x) = -f(x) \) for all \( x \).

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