Question

How do you know if `G(x) = sqrtx` is an even or odd function?

Answer 1

It is neither odd nor even.

Explanation:

Get `G(-x)`.

If `G(-x)=G(x)`, then it is even.

If `G(-x)=-G(x)`, then it is odd.

If neither is true, then it is neither odd nor even.

Solution

First, we restrict the domain of `G(x)` to `[0,+oo)`.

`" "G(-x)=sqrt(-x)`

However, `-x` will always be negative or `0`. So when you get the square root of `-x`, the answer will only either be `0` or imaginary.

Conclusion It is neither odd nor even.