Given the function f (x) = sin (Wx + π / 4), where w > 0, if the distance between two adjacent symmetrical axes of the function f (x) image is equal to π / 3, the analytic expression of the function is obtained And find the minimum positive real number m so that the function corresponding to m unit length of the function image is even

Minimum positive period = 2 * π / 3 = 2 π / 3
w=3
f(x)=sin(3x+π/4)
=sin(3(x+π/12))
m=π/12

RELATED INFORMATIONS

1. If the image of functions g (x) and f (x) = - 2x + 1 is symmetric with respect to y = x, then G (x)=___ Ask for detailed explanation
2. Let the image of two quadratic functions be symmetric with respect to the straight line x = 1, and the analytic expression of one function is y = x ＾ 2 + 2x + 1?
3. It is known that the image of F (x) = 2 ^ x, F1 (x), F2 (x), F3 (x), F4 (x) and the image of F (x) are symmetric about the X axis, Y axis, origin and line y = x respectively Try to write four function analytic expressions respectively
4. If the domain of F (x) is symmetric about the origin, then F1 (x) = f (x) + F (- x) is an even function and F2 (x) = f (x) - f (- x) is an odd function
5. F (x) = 1 + X / 1-x, F1 (x) = f (x), FK + 1 (x) = f [FK (x)], k = 1,2..., find F3 (x), F4 (x), F5 (x) I figured out that F1 (x) = 1 + X / 1-x, F2 (x) = - 1 / x, but F3 (x), F4 (x), F5 (x) are not big
6. If the even function y = f (x) decreases monotonically in the interval [0,4], then a f (- 1) > F (one third) > F (- 1) > b f (one third) > F (- 1) > F (- 1) > C f (- 1) > F (one third) > d f (- 1) > F (- 1) > F (one third) > F (one third)
7. Among the following functions, the function which is both even and monotonically decreasing on the interval (0,1) is () A. y=1xB. y=lgxC. y=cosxD. y=x2
8. Among the following functions, the function that is both even and monotonically increasing on the interval (0, + infinity) is A,y=x∧-1.B,y=log2x.C,y=|x| D,y=-x∧2
9. The even function y = f (x) decreases monotonically in the interval [0,4]. Compare the sizes of F (- 1), f (3 / π), f (- π)
10. Y = f (x) is defined in R, and its graph is symmetric with respect to the straight line x = A and x = B (a is not equal to b). It is proved that f (x) is a periodic function
11. It is known that ω > 0,0
12. Known w > 0,0
13. Given that the function y = 2Sin (Wx + Fei) is an even function (w ＞ 0,0 ＜ Fei ＜ π), the distance between two adjacent symmetry axes of an image is π 2, and f (π 9) is obtained After the image of the function is shifted to the right by π - 6 units, the decreasing interval of the function is obtained
14. The known function f (x) = 2Sin (Wx + φ) (W > 0, - π / 2)
15. It is known that y = 2Sin (Wx + a-pai / 6) 0
16. f(x)=x/(x^2+1) Does the equation f (x) - (x-1) / x = 0 have a root? If there is a root x0, ask for an interval (a, b) of length 1 / 4, so that XO ∈ (a, b). If not, explain the reason?
17. Given the function f (x) = 2Sin - (2x - π / 6), 1. Write the equation of symmetry axis, symmetry center and monotone interval of function f (x). 2. Find the maximum and minimum value of function f (x) in the interval [0, π / 2]
18. (related functions) Given the set a = {Y / y = x Square-1, X contained in R}, B = {X / y = root 2X-4}, then the intersection of a and B = -, the union of a and B=—— The result is {X / X is greater than or equal to 2}, and the next lattice is {X / X is greater than or equal to - 1}
19. If the function f (x) = 2ax2-x-1 has exactly one zero point in (0,1), then the value range of a is () A. （1，+∞）B. （-∞，-1）C. （-1，1）D. [0，1）
20. Given that the function g (x) = - x2-3, f (x) is a quadratic function, when x ∈ [- 1,2], the minimum value of F (x) is 1, and f (x) + G (x) is an odd function, the analytic expression of F (x) is obtained