Question: Let f(x + y) = f(x) + f(y) for all x and y and suppose that f is continuous at x = 0. (a) Prove

Let f(x + y) = f(x) + f(y) for all x and y and suppose that f is continuous at x = 0.
(a) Prove that f is continuous everywhere.
(b) Prove that there is a constant in such that f (t) = mt for all t (see Problem 43 of Section 0.5).

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