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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
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The correct answer is:
$-f(x)$
$-f(x)$
$f(a-(x-a))=f(a) f(x-a)-f(0) f(x)$
$=-f(x)\left[\because x=0, y=0, f(0)=f^2(0)-f^2(a) \Rightarrow f^2(a)=0 \Rightarrow f(a)=0\right]$.
$=-f(x)\left[\because x=0, y=0, f(0)=f^2(0)-f^2(a) \Rightarrow f^2(a)=0 \Rightarrow f(a)=0\right]$.
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