A real valued function f (x) satisfies t...

A real valued function `f (x)` satisfies the functional equation `f (x-y)=f(x)f(y)- f(a-x) f(a+y)` where 'a' is a given constant and `f (0) =1, f(2a-x)` is equal to :

A

`f (-x)`

B

`f (a) +f(a-x)`

C

`f (x)`

D

`-f(x)`

Verified by Experts

The correct Answer is:

D

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