(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I've to show that if f:R->R is continuous in x' then f is limited in a suitable environment of x'.

2. The attempt at a solution

My lecturer said we should use the following inequality

|f(a)|=<|f(a)-f(y)|+|f(y)|

But how should I go on, I know I have to show something like this:

It exists d>0: it exist c element of [x'-d, x'+d]=I ==> |f(x)|=<|f(c)| for every x in I.

But how should I go on?

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# Continuous => limited in region

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