f(x) = 1 + x + x²

Question

Determine whether the function is odd, even, or neither.

Answer 1

Determine whether the function, f = 1 + x + x^2, is odd, even, or neither.

A function is even when f(x) = f(-x)

Since f(x) = 1 + x + x^2 and f(-x) = 1 - x + x^2, then f(x) ≠ f(-x)

The function is not even.

A function is odd when –f(x) = f(-x)

Since f(x) = 1 + x + x^2, giving –f(x) = -1 – x – x^2, and f(-x) = 1 - x + x^2, then -f(x) ≠ f(x)

The function is not odd.

Conclusion: The function is neither odd nor even