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Math Help - f uniformly continuous -> |f(x)| < a|x| + b ?

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    f uniformly continuous -> |f(x)| < a|x| + b ?

    Let f:\Re \rightarrow \Re be a uniformly continuous function. Prove that there exist two positive constants a, b such that |f(x)| \leq a|x| + b for every x in \Re
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    Quote Originally Posted by Amanda1990 View Post
    Let f:\Re \rightarrow \Re be a uniformly continuous function. Prove that there exist two positive constants a, b such that |f(x)| \leq a|x| + b for every x in \Re
    This problem was answered here.
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