Let u = R, a = {x | x + 1 ≥ 0}, B = {x | x}

Let u = R, a = {x | x + 1 ≥ 0}, B = {x | x}

CUA is x less than or equal to - 1, B is a subset of CUA, then a must be less than - 1, which is the value range of A
Let the complete set be a real number set R, a = {x | 1 / 2 ≤ x ≤ 3}, B = {x | X & # 178; + a
(CRA) ∩ B = B, then B is a subset of CRA,
CRA={X|x3},
If a ≥ 0, then B is an empty set and B is a subset of CRA,
If a
The known set a = {x | - 4 ≤ x ≤ - 2}, B = {x | - x}
A={x|-4≤x≤-2},B={x|x=-4
If the even function f (x) defined on R increases monotonically in the interval [0, positive infinity], and f (2) > F (lgx), then the value range of X is
Because this function is even
And because it increases monotonically on [0, positive infinity],
So monotonically decreasing on [positive infinity, 0]
x> F (2) > F (lgx), 2 > lgx, x = 0
If the image of the function f (x) = (1-x ^ 2) &; (x ^ 2 + AX-5) is symmetric with respect to the line x = 0, then the maximum value of F (x)
The image is symmetric with respect to the line x = 0, x = 0 is the y-axis, f (x) is the even function, f (x) = (1-x ^ 2) & # 8226; (x ^ 2 + AX-5) = x ^ 2 + ax-5-x ^ 4-ax ^ 3-5X ^ 2 = - x ^ 4-ax ^ 3-4x ^ 2 + AX-5, the coefficient of odd power of even function = 0, a = 0, f (x) = - x ^ 4-4x ^ 2-5, let x ^ 2 = t > = 0f (x) = - T ^ 2-4t-5, the symmetry axis is t =
It is known that the function f (x) defined on real number R is an even function. When x ≥ 0, f (x) = - X & # 178; + 8x-3. Find the maximum value of F (x) on R and write the monotone interval of F (x)
If f (x) = - X & # 178; + 8x-3 = - (x-4) &# 178; - 13, then the maximum value of F (x) on R is - 13
When x
If the function f (x) = x & # 178; + (a + 2) x + 3, where x is on [a, b] (a
Is it to find the value of a and B
Axis of symmetry: - (a + 2) / 2 = 1
∴a=-4
B is a symmetric with respect to the line x = 1
∴b=1×2-a
=6
The function y = f (x) defined on R is even. When x ≥ 0, f (x) = - 4x2 + 8x-3. (I) when x < 0, find the analytic expression of F (x); (II) find the maximum value of y = f (x), and write the monotone interval of F (x) on R (without proof)
(I) let x ＜ 0, then - x ＞ 0, f (- x) = - 4 (- x) 2 + 8 (- x) - 3 = - 4x2-8x-3, (2 points) ∵ f (x) is an even function, when ∵ f (- x) = f (x), ∵ x ＜ 0, f (x) = - 4x2-8x-3. (5 points) (II) from (I) we know that f (x) = − 4 (x − 1) 2 + 1 (x ≥ 0) − 4 (x + 1) 2 + 1 (x ＜ 0)
Given the function y = ax ^ 2 + 2x + C, the symmetry axis of the image is a straight line x = 2, and the maximum value of the function is - 3, find a, C
-1/a=2,
(4ac-4)/4a=-3
Just ask
The steps to prove the monotonicity of function by monotonicity definition
Write down the steps
(1) Take any two values in the given interval and X1 > x2
(2) Calculate Y1 - Y2
(3) Factorization, determine the symbol
(4) Conclusion