Let f (x) be defined as R. if f (x + 1) and f (x-1) are both odd functions, then the function y = f (x) has at least one in the interval [0100]______ Zero

∵ f (x + 1) and f (x-1) are both odd functions ∵ f (- x + 1) = - f (x + 1) -- --- ① f (- x-1) = - f (x-1) -- --- ② from ① we know that f (x) is symmetric with respect to point (1,0) ∵ f (1) = 0, from ② we know that f (x) is symmetric with respect to point (- 1,0) ∵ f (- 1) = 0, from ② we get that

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