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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

Options

  1. A-f(x)
  2. Bf(x)
  3. Cf(a)+f(a-x)
  4. Df(-x)

Correct answer

A. -f(x)

Step-by-step solution

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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