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

1. 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 $\Re$

2. Originally Posted by Amanda1990
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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