A real valued function f(x) satisfies the functional equation f(x−y)=f(x).f(y)−f(a−x)f(a+y) for some given constant a and f(0) = 1 then f(2a−x) =

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f(x)

−f(x)

f(−x)

f(a)+f(a−x)

answer is B.

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Detailed Solution

Put x=y=0⇒f(a)=0 f(2a−x)=f(a−(x−a))=f(a).f(x−a)−f(a−a)fa+x-a=-fx

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