Question: Let E be a function satisfying E(0) = E'(0) = 1. Prove that if E(a + b) = E(a)E(b) for all a and b, then

Let E be a function satisfying E(0) = E'(0) = 1. Prove that if E(a + b) = E(a)E(b) for all a and b, then E is differentiable and E'(x) E(x) for all x. Find an example of a function satisfying E(a + b) = E(a)E(b).

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