Continuity of a Function

Calculus Level 2

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