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

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Answer 1 · 2015-09-12T14:19:04

It is neither.

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.

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