Friday, May 27, 2016

real analysis - f is linear and continuous at a point impliesf should be f(x)=ax, for some ainmathbbR

Let f be a real valued function defined on R such that f(x+y)=f(x)+f(y). Suppose there exists at least an element x0R such that f is continuous at x. Then prove that f(x)=ax, for some xR.


Hints will be appreciated.

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