If \( f(x-y), f(x) f(y) \), and \( f(x+y) \) are in A.P. for all \(...

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If \( f(x-y), f(x) f(y) \), and \( f(x+y) \) are in A.P. for all \( x, y \), and
P \( f(0) \neq 0 \), then

W.
(1) \( f(4)=f(-4) \)
(2) \( f(2)+f(-2)=0 \)
(3) \( f^{\prime}(4)+f^{\prime}(-4)=0 \)
(4) \( f^{\prime}(2)=f^{\prime}(-2) \)
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