Continuity of a Function

Calculus Level 3

Let f:RRf:\mathbb{R}\rightarrow\mathbb{R} satisfy f(x+y)=f(x)+f(y)  x,yRf(x+y)=f(x)+f(y)\ \forall\ x,y\in\mathbb{R}. If ff is continuous at x=0x=0, find the number of points of discontinuity of function ff.

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