Let $\displaystyle f:\Re \rightarrow \Re$ be a uniformly continuous function. Prove that there exist two positive constants a, b such that $\displaystyle |f(x)| \leq a|x| + b$ for every x in $\displaystyle \Re$
Let $\displaystyle f:\Re \rightarrow \Re$ be a uniformly continuous function. Prove that there exist two positive constants a, b such that $\displaystyle |f(x)| \leq a|x| + b$ for every x in $\displaystyle \Re$