I need to show that the function f(x)=|x|^1/2 is uniformly continuous on R. I know how to start it's just I get confused when it gets to f(x)-f(y). Any help would be appreciated.

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- Nov 10th 2010, 05:57 AMlennyProving a function is uniformly continuous on R
I need to show that the function f(x)=|x|^1/2 is uniformly continuous on R. I know how to start it's just I get confused when it gets to f(x)-f(y). Any help would be appreciated.

- Nov 10th 2010, 07:45 AMDrexel28
What have you tried? What can you use?

If you're allowed to use anything I'd note that on $\displaystyle [-1,1]$ $\displaystyle f$ is continuous and thus by the Heine-Cantor theorem uniformly continuous. Then, for $\displaystyle x\in\mathbb{R}-[-1,1]$ I'd note that $\displaystyle f'(x)$ is bounded and thus $\displaystyle f$ is Lipschitz and so evidently unif. cont.