On the small problem of function period If f (x-4) = - f (x), f (x) is an odd function, why can we get f (X-8) = f (x) -F (x-4) = f (X-8) why

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• 7. Dirichlet function On Baidu Encyclopedia The Dirichlet function over the real number field is expressed as: D(x)=lim(n→∞){lim(m→∞)[cosπm!x]^n} 　(1)　 It can also simply express the form of piecewise function d (x) = 0 (x is irrational) or 1 (x is rational) (2) The process of finding (1) and pushing (2)
• 8. Some problems on Dirichlet function For: 1. Is a periodic function, 3 is a period of it; 2. The equation f (x) = cosx has rational roots; 3. The equation f [f (x)] = f (x) has the same solution set as the equation f (x) = 1 In fact, Dirichlet function refers to: (1) when x is a rational number, f (x) = 1; (2) when x is an irrational number, f (x) = 0
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• 13. Let f (x) = cos (2 π − x) + 3cos (π 2 − x), then the minimum positive period of the function is () A. π2B. πC. 2πD. 4π
• 14. Two questions about the proof of periodic function 1. It is known that f (x) is an odd function, and the image of F (x) is symmetric with respect to the line x = 2. It is proved that f (x) is a periodic function 2. Let f (x) be an even function defined on R whose image is symmetric with respect to the line x = 1. For any x 1, x 2 belonging to [0,0.5], f (x 1 + x 2) = f (x 1) * f (x 2) is proved to be a periodic function
• 15. How to prove the periodic problem of two functions? If f (x) is an odd function and the equation f (a + x) = f (A-X) holds for all x ∈ R, it is proved that the period of F (x) is 4a If f (x) is symmetric with respect to (a, Y0) and x = B, it is proved that the period of F (x) is 4 (B-A)
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• 20. A mathematical problem, periodic function If f (x) is a function defined on the set of real numbers and f (x + 2) = f (x + 1) = f (x), f (1) = Lg3 / 2, f (x) = LG15 Prove by definition that it is a periodic function