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I've been given the following question but I'm unsure if there are actually any answers:

Give examples of functions $f,g: \mathbb{R}\to\mathbb{R}$ which are uniformly continuous such that $f$ is not bounded but $g$ is bounded.

I know that if $f:(a,b)\to\mathbb{R}$ is uniformly continuous then $f$ is bounded so surely there is no such example for $f$ ?

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What about $f(x)=x$ and $g(x)=A$?

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  • $\begingroup$ Wonderful. The shortest answers are the best answers. $\endgroup$ – Rudy the Reindeer Oct 27 '14 at 9:51
  • $\begingroup$ @MattN. Thanks! $\endgroup$ – Paul Oct 27 '14 at 9:54

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