Question

The function satisfies the identity f(x) + f(y) = f(x+y) (1) for all x and y. Show that 2f(x) = f(2x) and deduce that f '' (0) = 0. By considering the Maclaurin series for f(x), find the most general function that satisfies (1). [Do not consider issues of existence or convergence of Maaclaurin series in this question.]