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Let $f:\mathbb{R} \rightarrow \mathbb{R}$, be continuous at $\pi$ and satisfy $f(x + y) = f(x) + f(y)$ for all $x,y \in \mathbb{R}$. Determine $f.$

Stackman
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Todd
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    You can't "determine f". Both $f(x) = x$ and $f(x) = 0$ satisfies this relation, for instance. But you can find all such $f$, see this wikipedia article. – Arthur Oct 29 '18 at 10:30
  • I am curious as to why you deleted your question (& my answer) at https://math.stackexchange.com/questions/2974314/showing-monotone-nature-of-a-given-continuous-function/2974343?noredirect=1#comment6141630_2974343? – copper.hat Oct 29 '18 at 19:16

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If I have understood correctly the question you are asking to find a function which satisfy that property.

I would say that $f:\mathbb{R}\to\mathbb{R}$ defined as $f(x)=x$ for each $x\in\mathbb{R}$ works since $f(\pi)=\pi$ and $f(x+y)=x+y=f(x)+f(y)$ for each $x,y\in\mathbb{R}$.

anonymous
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