It is known that f (x) = x ^ 2 + (1-A) x-a (a belongs to R) proposition p: there exists x > - 1 so that x + 2 + F (x) 0 holds If P and Q are false, P or q are true, find the range of a! | Math enthusiast | Mathematical art

It is known that f (x) = x ^ 2 + (1-A) x-a (a belongs to R) proposition p: there exists x > - 1 so that x + 2 + F (x) 0 holds If P and Q are false, P or q are true, find the range of a!

①
∵f(x)=x²+(1-a)x-a
Proposition p: there exists x > - 1 such that x + 2 + F (x) 0
Δ=(-2a)²-12a0
a²-3a0
a(a-3)

Let function FX = xlnx + 4 (1) find monotone interval and extremum of function FX (2) if x 〉 = 1, there is always FX 〈 = ax ^ 2-ax + 4

(1) When x = 1 / E, the extremum is monotonically decreasing (1 / E, infinite) on (0,1 / E), and x = 1 / E is the minimum value (2). Let g (x) = ax ^ 2-ax + 4-xlnx-4 G '(x) = 2ax-a-1-lnx. When x > = 1, G' (x) > = 0 g (1) = 0 g (x) > = g (1) a > = (1 + LNX) / (2x-1), we can get the following formula

If the function y = a ^ 2x + 2A ^ X-1 (a > 1) has a maximum value of 14 on [- 1,1], then the value of real number a is

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1. If the maximum value of function y = a ^ (2x) + 2A ^ X-1 (a > 0, a ≠ 1) on interval [- 2,2] is 14, then the value of real number a is 14 Root 3, 3 / 3 root 3
2. Given that a and B are real numbers, the function f (x) = x ^ 2 + BX + C has the following properties for any α, β∈ R: F (sin α) ≥ 0, f (2 + cos β) ≤ 0 (1) Finding the value of F (1) (2) It is proved that C ≥ 3 (3) Let the maximum value of F (sin α) be 10, and find f (x) Request detailed process
3. Given that the point P (1,4) is on the circle C: x2 + Y2 + 2ax-4y + B = 0, the symmetric point of point P about the straight line x + Y-3 = 0 is also on the circle C, then a=______ ，b=______ ．
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8. On a highway, there is a warehouse every 100 km, with a total of five warehouses. No.1 warehouse has 10t goods, No.2 warehouse has 20t goods, No.34 warehouse has no goods, and No.5 warehouse has 40t goods. Now if you want to store all the goods in one warehouse, if you need 0.5 freight per ton of goods to transport 5 km, how much freight will it cost at least?
9. The problem of integral Simplification and calculation: 3（a+b-c)+8(a-b-c)-7(a+b-c)-4(a-b-c)
10. If one root of the quadratic equation AX ^ 2 + BX + C = 0 is greater than 1 and the other root is less than 1, then the value of a + B + C is
11. Let y = log2 (AX ^ 2-2x + 2) > 2 be constant on X, and find the value range of real number a
12. Given the complete set u = R, a = {X-2 ≤ x ≤ 5} B = {x M-1 ≤ x ≤ 2m + 1} if a ∩ B = &; find the range of M
13. If the corresponding points of 2m, m and 1-m on the number axis are arranged from left to right, then the value range of M is the same
14. Given that there is only one element in the set a = {x | x ∈ R | (A2-1) x2 + (a + 1) x + 1 = 0}, the value of a is obtained
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16. Let u = {(x, y) | x belong to R, y belong to R}, a = {(x, y) | 2x-y + a > 0}, B = {(x, y) | x + 2y-b ≤ 0}, then p (1,4) belongs to cub If and only if
17. If f (2x + 1) = x2 + 1, then f (0) = 0___ ．
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19. Let u = R, a = {x | 1 / X
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