Question

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

Answer 1

`f(x) = x^3-x^5` is odd.

Explanation:

A function `f` is even if `f(-x) = f(x)` and is odd if `f(-x) = -f(x)`. In this case, we have

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

`=-x^3+x^5`

`=-(x^3-x^5`

`=-f(x)`

Thus `f(x) = x^3-x^5` is odd.