Question

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

Answer 1

`F(x)=x^3-x` is an odd function.

Explanation:

A function is even if `F(–x)=F(x)` and

a function is odd, if `F(–x)=-F(x)`.

As we have `F(x)=x^3-x` and

`F(-x)=(-x)^3-(-x)=-x^3+x`

= `-(x^3-x)=-F(x)`

Hence `F(x)=x^3-x` is an odd function.