Continous function (prove)

**doug** · November 3rd 2010, 03:18 PM

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

Any help would be appreciated.

**Drexel28** · November 4th 2010, 05:32 PM

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 $x-y=\left(\sqrt[3]{x}\right)^3-\left(\sqrt[3]{y}\right)^3=\left(\sqrt[3]{x}-\sqrt[3]{y}\right)\left(x^{\frac{2}{3}}+\sqrt[3]{xy}+y^{\frac{2}{3}\right)$

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