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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)
(1) F (x) = xsquare - 5x + 10
(2).f(x)=2x
If you know the function y = (SiNx) ^ 4 + (2 radical 3) * SiNx * cosx - (cosx) ^ 4, change the function to y = asin (Wx + a) (a > 0, - Pie / 2)
(SiNx) ^ 4 - (cosx) ^ 4 = (SiNx) ^ 2 - (cosx) ^ 2 = - cos2x (square difference)
Root 3sin2x cos2x = 2Sin (2x Pai / 6)
How to change the function y = SiNx + cosx to y = asin (x + φ) + k?
y=sinx+cosx
＝√2（√2/2sinx+√2/2cosx)
＝√2sin(x+π/4)
Given the function y = 2 (SiNx) ^ 2 + 2 √ 3sinx * cosx-2, try to express the function as y = asin (ω x + φ) + B
The period, maximum and minimum of the function are obtained
y=2(sinx)^2+2√3sinx*cosx-2=1-cos2x+√3sin2x-2=√3sin2x-cos2x-1=2[(√3/2)*sin2x-(1/2)*cos2x]-1=2sin(2x-30°)-1
The period is π, the maximum is 1 and the minimum is - 3
RELATED INFORMATIONS
- 1. 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
- 2. 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]
- 3. 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
- 4. If f (x) = - x ^ 2 + 2aX and G (x) = (a + 1) ^ (1-x) are decreasing functions in the interval [1,2], find a
- 5. 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
- 6. 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········
- 7. 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___ ．
- 8. 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________
- 9. 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?
- 10. "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
- 11. It is proved that the function f (x) = 2 / 2 of X is an increasing function on (- infinity, 0)
- 12. It is known that the image of quadratic function y = ax & # - 178; + BX + C passes through point a (1,0) B (2, - 3) C (0,5) 1. Find the analytic expression of this quadratic function 2. The vertex coordinates of the quadratic function are obtained by the collocation method
- 13. Quadratic function f (x) = ax & # 178; + BX + C For any x ∈ R, is there a, B, C ∈ R, which satisfies that ① f (x-1) + F (- 1-x) = 0 and f (x) ≥ 0, and ② 0 ≤ f (x) - x It should be that there are 0 ≤ f (x) - x ≤ 1 / 2 (x-1) &;
- 14. If the minimum value of quadratic function y = x & # 178; - MX + 3 is - 3, then M=
- 15. Let f (x) = AX2 + BX + C have the maximum and minimum values of M and m respectively in the interval [- 2,2], and set a = {x ﹤ f (x) = x} (1) if a = {1,2} (2) if a = {2} and a ＞ 0, let g (a) = M-M and find the expression of G (a)
- 16. Given that the quadratic function f (x) = the square of AX + BX + C satisfies the condition f (- 1) = f (3) = 0, and the minimum value is - 8, the analytic solution of the function is obtained
- 17. Given that the quadratic function y = ax ^ 2-4x + 13A has a minimum value of - 24, then a
- 18. The minimum value of the quadratic function of one variable y = x2 ax + of X is 1 / 2
- 19. The following sets are represented by enumeration: ① a = {x | X & # 178; = 9} ② B = {x ∈ n | 1 ≤ x ≤ 2} ③ C = {x | X & # 178; - 3x + 2 = 0}
- 20. The solution equation is: (1) x ^ 2 + x = 0 (2) (X-2) (x-3) = 30