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

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−f(x)

f(x)

f(a)+f(a−x)

f(−x)

answer is A.

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Detailed Solution

f(a−(x−a))=f(a)f(x−a)−f(0)f(x) =−f(x)[∵x=0,y=0,f(0)=f2(0)−f2(a) ⇒f(a)=0]

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