Let f (x) be defined for all x > 0 and be continuous. Let f (x) satisfy fxy=f(x)−f(y) for all x, y and f (e) = 1. Then

Taking f (x) = log x, we see thatfxy=f(x)−f(y)Clearly, f (x) is not bounded and f1x=−log⁡x→∞ as x→0Also, x f (x) = x log x → 0 as x → 0The correct option is (3) and (4)