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The known set a = {x | x ^ 2-4mx + 2m + 6 = 0} B = {x | X3 / 2 or M
If a intersection B is not equal to an empty set, then x ^ 2-4mx + 2m + 6 = 0 has a solution (4m) ^ 2-4 (2m + 6) > = 0 (2 (M + 1) (2m-3)) > = 0 m3 / 2x ^ 2-4mx + 2m + 6, and the poles of x ^ 2-4mx + 2m + 6 are x = 2m. When the distance between the two roots and the poles is root sign (2 (M + 1) (2m-3)) m > 3 / 2, 2m > root sign (2 (M + 1) (2m-3)), that is to say, two roots > 0 are not equal to empty
Hello, the answer is right. For this problem, we should first determine "0" and get a range of M. And you didn't.
Secondly, as long as M-1 can guarantee a negative root, why do you choose-3? Right? You think about it.
It's not easy to adopt the answer. Question: isn't there a formula for inequality
Let a = {x | - 1 ≤ x ＜ 3} and B = {x | - x ≤ a}. If a intersects B and is an empty set, what is the value range of real number a
Because the intersection is empty, the maximum value of B is less than the minimum value of A. the maximum value of B is a, and the minimum value of a is - 1, so a
a＜-1
A
Set a = {x | x ^ 2-x-2
Please write down your thoughts!
A={x|x^2-x-2≤0}={x|-1≤x≤2}
B={x|x≤a}
Because a ∩ B is not an empty set
So a ≥ - 1
If you don't understand, please hi me, I wish you a happy study!
Add: This is the way of thinking, first solve a, and then draw the number axis to see, found that only when a is greater than or equal to - 1, there is intersection
The image of function f (x) and the image of G (x) = 2 ^ X are symmetric with respect to y = X. The maximum value of F (4x-x ^ 2) is?
From the meaning of the title
f(x)=log2(x)
therefore
f(4x-x^2)=log2(4x-x^2)
The maximum value of 4x-x ^ 2 is 4, so the maximum value of F (4x-x ^ 2) is log2 (4) = 2
Please explain the monotonicity of function f (x) = SiNx with the mathematical definition of function monotonicity
Forget to explain the domain interval: (- π / 2, π / 2).
Function monotonicity definition: if f (x) domain is (a, b), if for any x1, X2, a
If ABC is an equal ratio sequence, how many intersections does the image of the function y = ax ^ 2 + BX + C have with the X axis?
The image of the function has no intersection with the X axis
The number of intersections between image and x-axis is related to the value of △ if △ is greater than 0, there are two different intersections; if △ is equal to 0, there is one intersection; if △ is equal to 0, there is one intersection
On proving monotonicity of function by definition
For example, on this issue
It is proved that the function f (x) = - root x is a decreasing function in the domain of definition
Why can't we prove that f (x1) - f (x2) = root sign X2 - root sign X1 is a decreasing function
(when she asked her classmate, she said it was because she had to add steps. I don't think it's very reliable.)
I went online and said that I had committed "circular argument"
But how to make a circular argument!
If you directly say that the root sign X2 - the root sign X1 is greater than 0, it is obtained by using the conclusion that f (x) = the root sign x is an increasing function in the domain of definition. Therefore, it is suspected of circular argument. It is better to rationalize the molecule to get x1-x2 / the root sign X1 + the root sign X2, and then judge that the root sign X2 - the root sign X1 is greater than 0
If x + C is the intersection point of the sequence of quadratic numbers, then x + C is known
A. 0b. 0 or 1C. 1D. 2
From a, B, C into an equal ratio sequence, we get B2 = AC, and AC > 0, let AX2 + BX + C = 0 (a ≠ 0), then △ = b2-4ac = ac-4ac = - 3aC < 0, so the number of intersections between the image of function f (x) = AX2 + BX + C and X axis is 0
How to prove the monotonicity of function by definition?
Let any x 10, then we prove whether the sign of F (x 2) - f (x 1) is positive or negative, whether the sign is regular is monotonically increasing, and whether the sign is negative is monotonically decreasing
Given the image constant crossing point P of function y = 5A ^ (x + 2) - 6, if point P is on the line ax + by + 1 = 0 and ab > 0, then the minimum value of 1 / A + 2 / BD is?
When x = - 2, y = - 1
P(-2,-1)
Substituting it into the linear equation, we get the following results
-2A-B+1=0
B=1-2A
A(1-2A)>0
Zero
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