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

Question

3533 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-12T14:19:04

It is neither.

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

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

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

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

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

Is the function (2−x)13(2-x)^(1/3) even, odd or neither?