Question

Is the function `g(x) = x^3-5x` even, odd or neither?

Answer 1

Rather than using a particular number or numbers, the best method is to substitute `-x` and simplify.

Explanation:

To determine whether `g` if even, odd, or neither, evaluate `g(-x)`.

If `g(-x)` simplifies to `g(x)`, then `g` is even. If `g(-x)` simplifies to an equivalent to `-g(x)`, then `g` is odd. It may be neither even nor odd.

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

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

`= -x^3+5x`

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

`= -g(x)`.

So, `g` is odd.