Given that the images of power functions y = f (x) and y = g (x) pass through points (3,9) and (8,32), the solution set of inequality f (x) ≥ g (x) is

Given that the images of power functions y = f (x) and y = g (x) pass through points (3,9) and (8,32), the solution set of inequality f (x) ≥ g (x) is

F (x) = x ^ A, substituting (3,9) to get: 3 ^ a = 9, so: a = 2; so: F (x) = x & # 178;; G (x) = x ^ A, substituting (8,2) to get: 8 ^ a = 2, so: a = 1 / 3; so: G (x) = x ^ (1 / 3); f (x) > G (x), that is: X & # 178; > x ^ (1 / 3); from the image of power function, we can see that the solution set is (1, + ∞); hope to help

Let f (x) = AX2 + (B-1) x-a-ab, the solution set of inequality f (x) > 0 is (- 2, 0). (1) find the value of a and B; (2) find the maximum and minimum value of function g (x) = f (x) x2 + X − 2 on [2, 4]

(1) The solution set of ∵ f (x) > 0 is (- 2, 0), ∵ a < 0, and − B − 1A = − 2 − AA + ABA = 0 The results show that a = - 1B = - 1, f (x) = - x2-2x (6 points). (2) from (1), G (x) = − (x2 + 2x) x2 + X − 2 = − x (x + 2) (x + 2) (x − 1) = − XX − 1 = − x − 1 + 1x − 1 = − 1 − 1x − 1 (8) g (x) is an increasing function on [2,4] Then G (x) min = g (2) = - 2, G (x) max = g (4) = - 43 (12 points)

If the solution set of inequality ax & # 178; + bx-2 > 0 is (- 2, - 1 / 4), then a + B

The meaning of - 1 and - 1 / 4 are the following two parts of the equation AX ^ 2 + bx-2 = 0
Then - 1-1 / 4 = - B / A
-2×（-1/4）=-2/a
Then a = - 4, B = - 5
So a + B = - 9
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It is known that the solution set of inequality X & # 178; + ax + B < 0 is (1,2). Find the solution set of inequality BX & # 178; + ax + 1 > 0 about X

B = 1 × 2 = 2, - a = 1 + 2 = 3, a = - 3, so the following inequality: 2x & # 178; - 3x + 1 > 0, (2x-1) (x-1) > 0, so x > 1 or x < 1 / 2

Then the solution set of inequality ax > A is a < 0
Note: a < 0

Because the solution set of AA is:
x

The solution set of the inequality system 2x-a > 6 x + B < 4 is 0.5

2x＞a＋6
x＞（a＋6）/2=0.5
a＋6=1
a=-5
x＋b＜4
x＜4-b=3
b=1
therefore
5a-b=-25-1=-26

System of inequalities x > - 3 / 2, x-4-3 / 2, x-4

x> The smallest integer with - 3 / 2 greater than - 3 / 2 is - 1
x-4

To solve the system of inequalities, half X-5 ＞ 0, - 2x + 7 ＞ 3

1/2x-5＞0
1/2x>5
x>10
-2x+7＞3
2x

If the solution set of half of the inequality system x + a ＞ = 2 2x-b ＜ 3 is 0 ＜ = x ＜ 1, then the value of a + B? As long as the result is solved in ten minutes!

a=2,b=-1
a+b=1

If x ∈ R, the inequality KX & sup2; - KX + 1 > 0 holds, then the value range of K is

When k = 0, then the linear equation 1 > 0 holds, so K can be equal to 0
When k ≠ 0, then it's a quadratic equation of one variable. If we want to make the constant of K ≠ 0, then the parabolic equation should open up, otherwise the opening down can't all be greater than 0
So k > 0
This sub satisfies △ = (- K) ^ 2-4k