question_answer

A real valued function f(x) satisfies the functional equation \[f\,\,\left( x-y \right)=f\,(x)\,\,f(y)-f\,\,(a-x)\,\,f\,\,(a+y)\]where a is a given constant and f (0) = 1. Then \[f(2a-x)\] is equal to

A)  \[f(-x)\]            

B)  \[f(a)+f(a-x)\]

C)  \[f(x)\]                         

D)  \[-f(x)\]

E)  None of these