Let f (x) be an odd function on (- ∞, + ∞), f (x + 2) = - f (x). When 0 ≤ x ≤ 1, f (x) = x, then f (7.5) is equal to Why ∵ f (x + 2) = - f (x), ∵ f (x + 4) = f (x) ∵ f (7.5-8) = f (- 0.5)? Answer! | Math enthusiast | Mathematical art

Let f (x) be an odd function on (- ∞, + ∞), f (x + 2) = - f (x). When 0 ≤ x ≤ 1, f (x) = x, then f (7.5) is equal to Why ∵ f (x + 2) = - f (x), ∵ f (x + 4) = f (x) ∵ f (7.5-8) = f (- 0.5)? Answer!

This is a significant problem of periodic function. I will simply push it out, because f (x + 2) = - f (x) replaces x with - x to get f (- x + 2) = - f (- x). Because f (x) = - f (- x) gets f (x + 2) + F (2-x) = 0 gets f (x + 2) = - f (2-x) = f (X-2), replaces X-2 with X to get f (x + 4) = f (x), and then replaces x with x + 4 to get f (x + 8) = f (x)

RELATED INFORMATIONS

1. Let f (x) be an odd function on R, and f (x + 2) = - f (x). When 0 ≤ x ≤ 1, f (x) = x, then f (4.5) is equal to?
2. Let f (x) = 2x / (5x + 1) (x ∈ R, and X is not equal to - 1 / 5) Find: 1 inverse function F-1 (x); The range of 2F-1 (1 / 5) and F-1 (x)
3. Let f (x) = a ^ x + B (a > 0) (a is not equal to 1) g (x) = 2x ^ 2-5x-k. if f (x) > m is r-constant for X, then f (x) > m is r-constant The range of M is
4. Let f (x) = (1-2x3) 10, then f ′ (1) equals () A. 0B. 60C. -1D. -60
5. If f (0.5) = 9, then f (8.5) is equal to () A. -9B. 9C. -3D. 0
6. Given the function f (x) = {x2 + 1, (x is greater than or equal to 0), - 2x (x)
7. Given the function y = - 2x + 8, when x is equal to, y is greater than 4, when x is equal to, y is less than or equal to negative two
8. If the number of terms of the expansion of (1 + x) ^ n is odd and the coefficients of the fifth, sixth and seventh are equal difference, then what is n The title of binomial theorem
9. In (1 + x) + (1 + x) 2 + +In the expansion of (1 + x) 6, the coefficient of term X2 is______ (answer with numbers)
10. If the coefficient of x ^ 3 in the binomial expansion of (x ^ 2 + 1 / ax) ^ 6 is 5 / 2, then a =? explain
11. F (x) is an odd function on R, f (x = 2) = - f (x) when x is greater than or equal to 0 and less than or equal to 1, f (x) = x, f (7.5) =? F (x) is an odd function on R, f (x + 2) = - f (x) when x is greater than or equal to 0 and less than or equal to 1, f (x) = x, f (7.5) =?
12. Let f (x) be an odd function on R, and f (x + 2) = negative f (x). When x is greater than or equal to 0 and less than or equal to 1, f (x) = x, then what is f (7.5) equal to
13. What is the cubic C of quadratic B of negative 6A plus the cubic C of 2Ab
14. We know that P: F (x) = 1 − X3, and | f (a) | 2, Q: set a = {x | x2 + (a + 2) x + 1 = 0, X ∈ r}, and a ≠ r}. If P or q are true propositions, P and Q are false propositions, we find the value range of real number a
15. The known function f (x) = cos ^ 2 (x + π / 12) Let f (x) = 1 / 2 [1 + cos (2x + 6 / π)] How did you get here?
16. In (1 + x) ^ n, the sum of all odd binomial coefficients is 1024. What is the binomial coefficient of the middle term?
17. （1+x）+（1+x）+… +What is the sum of the coefficients in the expansion of (1 + x) ∧ 10
18. The coefficient of (x + 1) (x-1) ^ 5 expansion with x ^ 2 term is equal to
19. If x △ 5 is equal to y △ 6, then x is equal to () and Y is equal to () emergency
20. If - x equals + 6, then x = (); if y = - 1.5, then - y = ()