Relevant Equations: f (x+cy)=f (x)+cf (y), ∀x,y∈R, ∀c∈R. We need to show that lim x → a f ( x) = f ( a), ∀ a ∈ R . At first, I tried to show that f is continuous at 0 and from there I would show for all a∈R. But now, I think this may not even be true. I only got that f (0)=0. I'm very confused, I appreciate any help!

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