# Continous function (prove)

• November 3rd 2010, 03:18 PM
doug
Continous function (prove)
I am trying to prove that $\sqrt[3]{id_\mathbb{R}}$ function is continous.

Any help would be appreciated.
• November 4th 2010, 05:32 PM
Drexel28
Quote:

Originally Posted by doug
I am trying to prove that $\sqrt[3]{id_\mathbb{R}}$ function is continous.

Any help would be appreciated.

What precisely are you having trouble with? Notice that $x-y=\left(\sqrt[3]{x}\right)^3-\left(\sqrt[3]{y}\right)^3=\left(\sqrt[3]{x}-\sqrt[3]{y}\right)\left(x^{\frac{2}{3}}+\sqrt[3]{xy}+y^{\frac{2}{3}\right)$