"Mathematics function of senior one" asks all senior brothers and sisters to answer [if f (x) = x2 + BX + C, and f (1) = 0, f (3) = 0, find the value of F (- 1)] Note: 2 refers to the square

This topic is very simple, f (1), f (3) generation function simultaneous equations solution equation, get B, C value is OK

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1. Function equation f (x) - 2F (- x) = x ^ 2-5x, find f (x) The solution given by the answer is to construct another equation f (- x) + 2F (x) = x ^ 2 + 5x, but I don't know the basis of such construction?
2. Find the definition field (1) f (x) = loga (1 + 3x-4x ^ 2) (a > 1 and a ≠ 1); (2) f (x) = [LG (2x ^ 2 + 5x-12)] / √ (x ^ 2-3)
3. Let f (x) = 2mcos ^ 2x-2 √ 3msinx * cosx + n (M > 0) be defined as [0, Pai / 2] range [1,4] (1) (2) if f (x) = 2, find X
4. Let f (x) be a quadratic function, and f (x-1) + F (2x + 1) = 5x ^ 2 + 2x, find f (x)
5. It is known that f (x) = x & sup2; - (K-2) x + K & sup2; + 3K + 5 has two zeros if the two zeros of the function are α and β, Find the value range of α & # 178; + β & # 178
6. Given the function f (x) = (k ^ 2 + 1) x ^ 2-2kx - (k-1) ^ 2 (K ∈ R), X1 and X2 are the two zeros of F (x), and X1 > x2（ Given the function f (x) = (k ^ 2 + 1) x ^ 2-2kx - (k-1) ^ 2 (K ∈ R), X1 and X2 are the two zeros of F (x), and X1 > x2 (1) (I) prove: X1 = 1; (II) find the value range of x2; (2) Let g (k) be the minimum value of function f (x). When x 2 ∈ [- 2, - 1], find the maximum value of G (k)
7. Given the function f (x) = sin2x + acos2x (a ∈ R), and π / 4 is the zero point of the function y = f (x). (1) find the value of a, and find the function f (x) It is known that the function f (x) = sin2x + acos2x (a ∈ R), and π / 4 is the zero of the function y = f (x) (1) Find the value of a and the minimum positive period of function f (x); (2) If x ∈ [0, π / 2], find the range of function f (x)
8. The domain of definition of function f (x) is d. if f (x1) ≤ f (x2) exists for any x1, X2 ∈ d when X1 < X2, then function f (x) is called non decreasing function on D, Let f (x) be a non decreasing function on [0,1] and satisfy the following three conditions: ① f (0) = 0, ② f (1-x) + F (x) = 1, ③ f (x / 3) = 1 / 2F (x), then the value of F (1 / 3) + F (5 / 12) is___________ .
9. The minimum value of quadratic function x2 + 4x + 1
10. If the minimum value of quadratic function y = x ^ 2 + 4x + A is 2, then the value of a is 2__
11. I have two questions. 1. Do odd functions have f (0) = 0? Why? two Given function f (x) has f (y + x) = f (x) + 2Y (x + y) for any real number x, y Cut f (1) = 1, find the analytic expression of F (x) That's what I did F（1+Y）=F（1）+2Y（1+Y） Let 1 + y = T. replace y = T-1 Replace the above formula to get 2T square - 2T = 1 But the answer is 2x squared - 1 What's wrong with me, I know algebra, but why not?
12. 1. Positive scale function y = 1 / 2x_____ The value of quadrant y decreases with the decrease of X_____ 2. If the image with positive scale function y = KX (k is not equal to 0) passes through the point (1 / 3, - 1 / 2), then the image passes through the point______ Quadrant, K=______ 23. If the image with positive scale function y = x / m-2 passes through the second and fourth quadrants, the value range of M is________
13. The image of a certain function passes through the point (- 1,2), and the value of function y decreases with the increase of independent variable x. please write a function relation that meets the above conditions___ ．
14. Given that the cube-12x + 8 of the function f (x) = x has the maximum and minimum values m and m respectively in the interval [- 3,3], then M-M = () It's like taking the derivation as an odd function, and then it won't work········
15. It is known that the maximum value of the function f (x) = a ^ x (a > 0, and a ≠ 1) in the interval [1,2] is m, and the minimum value is n 1, if M + n = 6, find the value of real number a If M = 2n, find the value of real number a Wait online
16. If f (x) = - x ^ 2 + 2aX and G (x) = (a + 1) ^ (1-x) are decreasing functions in the interval [1,2], find a
17. If the function f (x) = SiNx + | SiNx |, X ∈ [0,2 π] has only two different intersections with the line y = k, then the value range of K is
18. If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is () A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]
19. Given the function f (x) = (SiNx cosx) SiNx, X belongs to R 1. Change it into the form of asin (Wx + a) + B. 2. Find the period
20. Find the following function analytic formula (1) known f (x + 1) = x & # 178; - 3x + 2 find f (x) (2) known f ((radical x) + 1) = 2 + 2 (radical) x find f (x)