Question: 4. Let f: R - R be a function. Suppose it satisfies, for all x, y E R f ( x + y) =f(x)+f(y) f

4. Let f: R - R be a function. Suppose it satisfies, for all x, y E R f ( x + y) =f(x)+f(y) f (xy) = f(x)f (y) a. Show that f (0) = 0 (Hint: let y = 0) b. Show that if x 2 0 then f (x) 2 0 c. Show that f is an odd function (i.e. f(-x) = -f (x) for all x) and hence that f is increasing [6 marks]

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