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 :

Question

( A ) $f(a) + f(a-x)$
( B ) $-f(x)$
( C ) $f(x)$
( D ) $-f(x)$