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