Given that x is a real number, find the value range of (x2 + 2x + 3) / (x2 + 2x + 1)

Given that x is a real number, find the value range of (x2 + 2x + 3) / (x2 + 2x + 1)

The original formula is the square of 1 + 2 / (x + 1), so the range of the original value is from 1 to positive infinity

Let f (x) = x2-2x + a have a zero point in the interval (2,3), then the value range of real number a is______ ．

∵ the symmetry axis of quadratic function f (x) = x2-2x + A is x = 1, the opening is upward, as shown in the figure; and the function f (x) & nbsp; has a zero point in the interval (2, 3). Combining with the image, we get f (2) < 0, f (3) > 0, and the solution is - 3 < a < 0. So the answer is: (- 3, 0)

If x0 belongs to R, log2m > |x0-1 | + |x0 + 1 |, then the value range of real number m is

|x0-1|+|x0+1|
=|x0-1|+|-x0-1|≥|x0-1-x0-1|=2
So log2 (m) > 2
log2(m)>log2(4)
m>4

12. Given proposition p: "for any x ∈ R, there exists m ∈ R, 4 * x + 2 * XM + 1 = 0". If proposition p is not a false proposition, then the value range of real number is————
Who can be counted is who

It is confirmed that the scope of M is that non-p is a false proposition, so p is a true proposition
Equation 4 * x + 2 * XM + 1 = 0 has real root equivalent 2 ^ x · M = - (4 ^ x + 1)
M = - (2 ^ x + 1 / 2 ^ x) total solution
∵ - (2 ^ x + 1 / 2 ^ x) ≤ - 2, so m ≤ - 2