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 ( 2 a − x ) is equal to

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f ( a − ( x − a )) = f ( a ) f ( x − a ) − f ( 0 ) f ( x ) = − f ( x ) [ ∵ x = 0 , y = 0 , f ( 0 ) = f 2 ( 0 ) − f 2 ( a ) ⇒ f 2 ( a ) = 0 ⇒ f ( a ) = 0 ] .

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