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

Sep 25, 2015

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 $g \left(- x\right)$.

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

$g \left(x\right) = {x}^{3} - 5 x$

$g \left(- x\right) = {\left(- x\right)}^{3} - 5 \left(- x\right)$

$= - {x}^{3} + 5 x$

$= - \left({x}^{3} - 5 x\right)$

$= - g \left(x\right)$.

So, $g$ is odd.