Question

How do you determine if `1/(x^3+1)` is an even or odd function?

Answer 1

Evaluate `f(2)` and `f(-2)` to show that it is neither.

Explanation:

A function is even if `f(-x) = f(x)` for any `x`

A function is odd if `f(-x) = -f(x)` for any `x`

In our example, let `f(x) = 1/(x^3+1)`

We find:

`f(2) = 1/(8+1) = 1/9`

`f(-2) = 1/(-8+1) = 1/-7 = -1/7`

So neither `f(-x) = f(x)` for any `x`, nor `f(-x) = -f(x)` for any `x`.

So this function is neither even nor odd.