80.Let f be a function such that f(x + y) =f(x) +f(y), x,y∈ R Show that if f is continuous at x = 0, then it is continuous everywhere.
Here f(x + y) = f(x) + f(y) ∀ x, y∈ R ..(1) Let f be continuous at x = 0 ⇒ f is continuous at x = c But c is any real number ∴ f is continuous ∀ .x ∈ R.
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