f(x) is a real valued function where f(xy) = [f(x)] + [f(y)] + f(x)f(y) for all

Question

F(x) is a real valued function where f(xy) = [f(x)] + [f(y)] + f(x)f(y) for all real x,y. If f(2) = 1, then what is the value of f(1/2) ?

Answer: Option E
:
E
Option (e)f(2) = f(2 x 1) = f(2) + f(1) + f(2).f(1) = 1f(1) = 0

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