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Math Help - Proving a function is uniformly continuous on R

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    Proving 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.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by lenny View Post
    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.
    What have you tried? What can you use?

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