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Let $$f : R \rightarrow R$$ be a function such that$$f(x + y) = f(x) + f(y), \forall x, y \in R$$If f(x) is differentiable at x = 0, Then
f(x) is differentiable only in a finite interval containing zero
f(x) is continuous $$\forall x \in R$$
f '(x) is constant $$\forall x \in R$$
f(x) is differentiable except at finitely many points
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