Question

How do you determine if `f(x)=1+3x^3-x^5` is an even or odd function?

Answer 1

Relate `f(-x)` with `f(x)`.

Explanation:

`f(-x) = 1 + 3(-x)^5 - (-x)^5`

`= 1 - 3x^5 + x^5`

If `f(-x) = f(x)`, `f(x)` is an even function. That is not the case.

If `f(-x) = -f(x)`, `f(x)` is an odd function. That is not the case.

Therefore, `f(x)` is neither an odd nor an even function.