Question

How do you determine whether `(2-x)^(1/3)` is an odd or even function?

Answer 1

`(2-x)^(1/3)` is neither even nor odd.

Explanation:

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

Then, letting `f(x) = (2-x)^(1/3)` we have

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

Thus `f(-x) != f(x)` and `f(-x) != -f(x)`

and so `(2-x)^(1/3)` is neither even nor odd.