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

It is neither.

#### Explanation:

Set $f \left(x\right) = {\left(2 - x\right)}^{\frac{1}{3}}$

If it was odd it should be $f \left(- x\right) = - f \left(x\right)$ hence

$f \left(- x\right) = {\left(2 - \left(- x\right)\right)}^{\frac{1}{3}} = {\left(2 + x\right)}^{\frac{1}{3}}$ so it isnt odd

If it was even then $f \left(- x\right) = f \left(x\right)$ hence

$f \left(- x\right) = {\left(2 - \left(- x\right)\right)}^{\frac{1}{3}} = {\left(2 + x\right)}^{\frac{1}{3}}$ so it isnt even as well.