(2007) the function f (x) defined on R is both an odd function and a periodic function, and t is a positive period. If the number of roots of the equation f (x) = 0 on the closed interval [- t, t] is n, then n may be () A. 0B. 1C. 3D. 5

Because the function is odd, in the closed interval [- t, t], there must be f (0) = 0, ∵ t is a positive period of F (x), so f (0 + T) = f (0) = 0, that is, f (T) = 0, so f (- t) = - f (T) = 0, ∵ - t, 0, t are the roots of F (x) = 0. If there is no root on (0, t), then there will always be f (x) > 0 or F (x) < 0. If f (x) > 0, then if x ∈ (- t, 0), f (x) > 0（ x) There is a contradiction between F (x) = f (x + T) > 0. F (x) = 0 has at least one root on (0, t). Since f (- T2) = - f (T2) = f (T2), f (− T2) = f (T2) = 0, there is also at least one root on (- t, 0), and there are at least five roots

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