Given that the range of F (x) = 2x ^ 2 + ax + B / x ^ 2 + 1 is [1,3], find the value of a and B

Given that the range of F (x) = 2x ^ 2 + ax + B / x ^ 2 + 1 is [1,3], find the value of a and B

The range y = 2x ^ 2 + ax + B / x ^ 2 + 1 (Y-2) x & # 178; - ax + (y-b) = 0 can be solved by the discriminant method. Because the equation can solve x, so Δ≥ 0A & # 178; - 4 (y-b) (Y-2) ≥ 04y & # 178; - 4 (2 + b) y + 8b-a & # 178; ≤ 0, the range is [1,3], so the solution set of inequality is [1,3]. From the root relation, 2 + B = 1 + 3 (8b-a & # 178

Given the function y = √ - X & # 178; + 2x + 3, find the domain of definition, range of value and monotone interval of the function

The bracket should be added. Is it y = √ (- x ^ 2 + 2x + 3)?
Domain: - x ^ 2 + 2x + 3
=-(x^2-2x-3)
=-(x^2-2x+1-4)
=-(x^2-2x+1)+4
=-(x-1)^2+4
We can get - (x-1) ^ 2 + 4 > = 0, (x-1) ^ 2

The monotone increasing interval of function f (x) = x & # 178; + 2x is? And the range is?

f(x)=x²+2x+1-1
=(x+1)²-1
Monotonically increasing when ∧ x > - 1
f(x)>=-1
The value range is [- 1, ∞)