Given the function f (x) = (M + 1) x ^ 2 - (m-1) x + M-1, if M belongs to (- 1,1) inequality and the solution set of F (x) > 0 is r, the value range of X is obtained Please give the detailed process, thank you, this kind of question is a little dizzy, usually is to find the scope of M, thank you!

Given the function f (x) = (M + 1) x ^ 2 - (m-1) x + M-1, if M belongs to (- 1,1) inequality and the solution set of F (x) > 0 is r, the value range of X is obtained Please give the detailed process, thank you, this kind of question is a little dizzy, usually is to find the scope of M, thank you!

f(x)=(m+1)x^2-(m-1)x+m-1
M is regarded as an independent variable,
g(m)=(x^2-x+1)m+(x^2+x-1)
∵x^2-x+1=(x-1/2)^2+3/4≥3/4>0
Let g (m) be an increasing function on (- 1,1),
M ∈ (- 1,1), G (m) > 0
Only G (- 1) = 2x-2 ≥ 0
So x ≥ 1

Let a > 0 and a ≠ 1, the inequality 2loga (4-A ^ x) ≤ loga [4 (a ^ x-1)]
Loga is a logarithm based on a

Log a (4-A ^ x) ^ 2 ≤ log a [4 (a ^ x-1)] where 1 ≤ a ^ x ≤ 4
When 0 ＜ a ＜ 1, the original formula can be (a ^ x-4) ^ 2 ≥ 4 (a ^ x-1) a ^ (2x) - 12a ^ x + 20 ≥ 0
That is, (a ^ X-10) (a ^ X-2) ≥ 0, a ^ x ≥ 10 or 0 ≤ a ^ x ≤ 2
Because 0 < a < 1 and 1 ≤ a ^ x ≤ 4, loga2 ≤ x ≤ 0
When a > 1, loga2 ≤ x ≤ loga4 can be obtained as above

Given the function FX = 2x + B / x + C, and F1 = 5, F2 = 6 (1), find the value of B.C. (2) prove that the function FX is a decreasing function in the interval (0,1)

The first problem is substituting to get b = 2, C = 1. The second problem is deriving the function to get the derivative function of the square (0,1) of F 'x = 2-2 / X is constant less than 0, so it is a decreasing function