If f (x) is defined as a function on R, and f (10 + x) = f (10-x), f (20-x) = - f (20 + x), it is proved that f (x) is an odd function and periodic function

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• 1. On the graph of the function y = 3 ^ X and y = Log1 / 3 1 / X_ symmetric On the graph of the function y = 3 ^ X and y = Log1 / 3 1 / X____ symmetric
• 2. Find function definition field y = log3 [Log1 / 3 (log3x)]
• 3. The set composed of the intersection points of the images of the linear function y = x + 3 and y = - 2x + 6 is () A. {4，1}B. {1，4}C. {（4，1）}D. {（1，4）}
• 4. The number of intersections of the graph of function y = f (x) and x = 2 () A. 0 B. 1 C. 0 or 1 D. not sure
• 5. The number of intersections between the image and the X axis of the function f (x) = x * LG (x + 2) - 1 is ()
• 6. How many intersections are there between the image of function y = x ^ 2-3 / X-1 / - 1 and X axis
• 7. 1. Function y = - x2 + X-1 how many intersections are there between image and X axis 3. The vertex coordinates of the function y = - 1 / 2 (x + 1) 2 + 2 are 4. According to the following conditions, find the analytic expression of quadratic function. (1) the image passes through points (1, - 2), (0, - 3), (- 1, - 6); (2) When x = 3, the function has a minimum value of 5 and passes through points (1,11); (3) The function image intersects the x-axis at two points (1 - √ 2,0) and (1 + √ 2,0), and intersects the y-axis at (0, - 2)
• 8. Function f (x) = 1 + X + x ^ 2 / 2 + x ^ 3 / 3?
• 9. The number of intersections between the image and the x-axis of the function f (x) = 13x3-x2-3x-1 is______ One
• 10. The coordinates of the intersection a of the image of function y = 3x + 1 and X axis are, and the coordinates of the intersection B of function y = 3x + 1 and Y axis are
• 11. 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
• 12. The even function y = f (x) decreases monotonically in the interval [0,4]. Compare the sizes of F (- 1), f (3 / π), f (- π)
• 13. 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
• 14. 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
• 15. 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)
• 16. 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
• 17. 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
• 18. 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
• 19. 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?
• 20. 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