Given the function f (x) = {0, X ∈ {XLX = 2n + 1, n ∈ Z} 1, X ∈ {XLX = 2n, n ∈ Z}, find f (f (- 3)) As shown in the figure, there is a moving point P on the edge of the square ABCD with side length of 4. Starting from point B, it moves along the broken line bcda to point A. set the moving distance of point P as X and the area of △ ABP as S (1) To find the analytic expression, domain of definition and range of value of the function s = f (x) (2) Find the value of F (f (3)) Let f (x) = {the cube root X of X + 2x + 2 ∈ (- ∞, 1) The third power of X + the negative third power of X ∈ (1, + ∞) Find f (f (0))

Given the function f (x) = {0, X ∈ {XLX = 2n + 1, n ∈ Z} 1, X ∈ {XLX = 2n, n ∈ Z}, find f (f (- 3)) As shown in the figure, there is a moving point P on the edge of the square ABCD with side length of 4. Starting from point B, it moves along the broken line bcda to point A. set the moving distance of point P as X and the area of △ ABP as S (1) To find the analytic expression, domain of definition and range of value of the function s = f (x) (2) Find the value of F (f (3)) Let f (x) = {the cube root X of X + 2x + 2 ∈ (- ∞, 1) The third power of X + the negative third power of X ∈ (1, + ∞) Find f (f (0))

1. F (- 3) = 0, f (0) = 1, so f (f (- 3)) = 12. S = f (x) = 2x x ∈ [0,4) 8 x ∈ [4,8) 24-2x x ∈ [8,12) 0 x ∈ [12,16] f (3) = 6, f (6) = 6, so f (3)) = 83. The cube root of cubic + (2 * 0 + 2) of F (0) = 0 = cubic root 2F (cubic root 2) = 2 + 1 / 2 = 2.5, so f (f (0)) = 2

1. It is known that f (x) is an even function, which is a decreasing function on [0, positive infinity). If f (lgx) > F (1), then the value range of X is
2. Given that the three vertices of △ ABC are a (1,3 / 2), B (4, - 2), C (1, y), and the center of gravity is g (x, - 1), then the values of X and y are
3. The function f (x) defined on the positive real number set satisfies the following conditions: 1) f (a) = 1 (a > 1) 2) if x ∈ R ^ +, f (x ^ m) = MF (x)
(1) Prove f (XY) = f (x) + F (y)
(2) It is proved that f (x) is monotonically increasing on the set of positive real numbers

1. It is known that f (x) is an even function, which is a decreasing function on [0, positive infinity). If f (lgx) > F (1), then the value range of X is
∵ f (x) is an even function
∴f(-x)=f(x）=f(|x|)………… Using this formula, we can avoid discussing the positive and negative of X
F (lgx) > F (1) can be reduced to f (| lgx |) > F (1),
∵ it is a decreasing function on [0, + ∞)
∴|lgx|

1. It is known that the domain of F (x) is (- 1,1) (1) the domain of F (x + 2) (2) the domain of F (3x + 5)
2. It is known that the domain of F (x) is (0,3) (1) the domain of F (x) (2) the domain of F (x-3)
3. The domain of F (x-1) is known as (1,4) (1) the domain of F (3x + 1) (2) the domain of F (2x ^ 2-2)
2. Is a known f (x + 2) domain (0,3)

1.
（1）（-3,-1）
（2）（-2,-4/3）
two
（1）（0,3）
（2）（-3,0）
three
（1）（-1/3,2/3）
(2) (- 1,1) (- radical (5 / 2), radical (5 / 2))

The circumference of circle C is 4 π, and it is tangent to the straight line 3x-4y-2 = 0, and the straight line 3x-y + 2 = 0 passes through the center of circle C

The circumference of the circle C is 4 π, so the radius of the circle is 2. Because the circle is tangent to the straight line 3x-4y-2 = 0, the distance from the center of the circle to the straight line is equal to the radius of the circle. Let the coordinates of the center of the circle be (a, b)
Then | 3a-4b-2 | / 5 = 2 (1)
And because the center of the circle is on the line 3x-y + 2 = 0, so 3a-b + 2 = 0 (2)
By solving the above equations, a = 0, B = 2 or a = - 20 / 9, B = - 14 / 3 can be obtained
So the standard equation of circle is x ^ 2 + (Y-2) ^ 2 = 4 or (x + 20 / 9) ^ 2 + (y + 14 / 3) ^ 2 = 4

Let the opposite sides of the inner angles a, B, C of the acute triangle ABC be a, B, C, a = 2bsin a (I) find the size of B; (II) if a = 33, C = 5, find B

(I) from a = 2bsina, according to the sine theorem, Sina = 2sinbsina, so SINB = 12, from △ ABC as an acute triangle, B = π 6. (II) according to the cosine theorem, B2 = A2 + c2-2accosb = 27 + 25-45 = 7. So, B = 7

1. Let f (x) = x ^ 2 + ax + B, a = {x | f (x) = x} = {a}, find the value of a and B
2. If f (x) is an increasing function defined on (0, + ∞), and for all x, Y > 0, f (x / y) = f (x) - f (y)
Finding the value of F (1)
If f (6) = 1, solve the inequality f (x + 3) - f (1 / 3)

1. A = {x | f (x) = x} = {a}, that is, x = a is the unique solution of the equation f (x) = x, X & sup2; + ax + B = XX & sup2; + (A-1) x + B = 0, a + a = - (A-1) a × a = B solution is obtained from Weida theorem, a = 1 / 3, B = 1 / 9 test X & sup2; + (1 / 3) x + (1 / 9) = x (x-1 / 3) & sup2; = 0, x = 1 / 3 is the unique solution, so a = 1 / 3, B = 1 / 9 meet the requirement 2

The trigonometric function value of special angle is used to calculate:
(1) Cos 105-sin 105
(2) Sin20 degree sin10 degree cos10 degree sin70 degree

(1)cos²105º-sin²105º=cos(2·105º)=cos210º=cos(180º+30º)=-cos30º=-(√3)/2
(2)sin20ºsin10º-cos10ºsin70º=sin10ºcos70º-cos10ºsin70º=sin(10º-70º)=sin(-60º)=-sin60º=-(√3)/2

Given the complete set u = R, and a = {x | X-1 | > 2 |}, B = {the square of X | x-6x + 8 = 0}, then the complement of a to u ∩ B is equal to?:
A.【1,4） B.（2,3） C.（2,3】 D.（1,-4）
PS: more than 2 and less than or equal to 3
Q:

The answer is wrong, or set B = change
If there is an absolute value, both sides of the inequality sign will be squared at the same time

1. If the intersection of the line 5x + 4Y = 2m + 1 and the line 2x + 3Y = m is in the fourth quadrant, then the value range of M is ()
A.m3/2 C.m

1. If the intersection of the line 5x + 4Y = 2m + 1 and the line 2x + 3Y = m is in the fourth quadrant, then the value range of M is (D. - 3 / 2)

1. Given the set a = {x | X & sup2; - ax + A & sup2; - 19 = 0}, B = {x | X & sup2; - 5x + 8 = 2}, C = {x | X & sup2; + 2x-8 = 0}, if the empty set is really contained in a ∩ B, and a ∩ C = empty set, find the value of A
2. Given the set a = {2,4, a cubic - 2A & sup2; - A + 7}, B = {- 4, a + 3, a & sup2; - 2A + 2, a cubic + A & sup2; + 3A + 7}, if a ∩ B = {2,5}, find the value of real number a, and find a ∪ B

1: B = {2,3} C = {- 4,2} because an empty set is really contained in a ∩ B, so a ∩ B is not an empty set, a ∩ C = an empty set can be obtained: there are elements in a in B, and there are no elements in a in C, so 3 is a solution in a, and a = 5 or - 25 is not satisfied, so a = - 22: because a ∩ B = {2,5}, a cubic - 2A & sup2; - A + 7 = 5, a + 3, a & sup2; -