Consider a function f : D → R, where D C R. Suppose the function satisfies the property f(xy) = f(x) + f(y) and that f(x) is not zero for all x € D. (a) By choosing suitable values of x and y, and making no other assumptions, show that domain D cannot contain 0 and that f(1) = 0. (b) Assuming that f is differentiable, find f'(x) in terms of f'(1). Hence show that dt [² t/t . t 1 f(x) = f'(1)

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