Question

How do you determine if `3sqrtx` is an even or odd function?

Answer 1

`3sqrt(x)` is neither even nor odd.

Explanation:

A function `f` is even if `f(-x) = f(x)` and odd if `f(-x) = -f(x)`.

In this case, though, for any `x in RR` where `x!=0`, we have that one of `sqrt(x)` and `sqrt(-x)` is real, and the other is imaginary. Thus, in all such cases, `3sqrt(-x)!=3sqrt(x)` and `3sqrt(-x)!=-3sqrt(x)`, meaning `3sqrt(x)` is neither even nor odd.