question_answer

If \[f(x-y)=f(x).g(y)-f(y).g(x)\] and \[g(x-y)=g(x).g(y)-f(x)\] for all \[x,\]\[y\in R.\] If right hand derivative at x = 0 exists for f(x). Find derivative of g(x) at x = 0.

A)  4                                

B)  3

C)  1                                

D)  0

E)  None of these