# Is the function f(s) = 4s^(3/2)  even, odd or neither?

Oct 21, 2015

Neither.

#### Explanation:

As a Real valued function $f \left(s\right)$ is only defined for $s \ge 0$, so it's neither odd nor even.

As a Complex valued function we find:

If $s \ge 0$ then $f \left(s\right) \ge 0$

If $s < 0$ then:

$f \left(s\right) = 4 {\sqrt{s}}^{3} = 4 {\left(i \sqrt{- s}\right)}^{3} = - 4 i \sqrt{- s} = - i f \left(- s\right)$

So neither $f \left(- s\right) = - f \left(s\right)$ nor $f \left(- s\right) = f \left(s\right)$