If the function \( f: \mathbb{R} \rightarrow \mathbb{R} \) satisfies the relation \( f(x)+f(x+4)....

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If the function \( f: \mathbb{R} \rightarrow \mathbb{R} \) satisfies the relation \( f(x)+f(x+4)=f(x+2)+f(x+6) \) for all \( x \in \mathbb{R} \),
\( \mathrm{P} \)
then a period of \( f \) is
(1) 3
(2) 7
(3) 5
(4) 8


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