Question

Is the function `(2-x)^(1/3)` even, odd or neither?

Answer 1

It is neither.

Explanation:

Set `f(x)=(2-x)^(1/3)`

If it was odd it should be `f(-x)=-f(x)` hence

`f(-x)=(2-(-x))^(1/3)=(2+x)^(1/3)` so it isnt odd

If it was even then `f(-x)=f(x)` hence

`f(-x)=(2-(-x))^(1/3)=(2+x)^(1/3)` so it isnt even as well.