Question

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

Answer 1

It isn't even nor odd.

Explanation:

To see if a function is even or odd, you must evaluate `f(-x)`, and there are three possibilites:

1. If `f(-x)=f(x)`, the function is even;
2. If `f(-x)=-f(x)`, the function is odd;
3. Otherwise, it's none of the two.

In this case,

`f(-x)=1/(-x^3+1)`, which is not equal to the original function, and it's neither its opposite (which would be `1/(-x^3-1)`). So, the function is not even nor odd