If the inequality | X-1 | + | X-2 | < m of X has a solution, then the value range of M is___ 1. If the inequality | X-1 | + | X-2 | < m of X has a solution, then the value range of M is___ 2. Let the image of F (x) be symmetric about y axis and monotone function when x > 0, then the sum of all x satisfying f (x) = f (x + 3 / x + 4) is___ 3. Find the range of function f (x) = x ^ 2-4x + 3 / 2x ^ 2-x-1 4. If 3f (x-1) + 2F (1-x) = 2x, find the analytic expression of F (x) 5. If the range of function f (x) = x ^ 2-4ax + 2A + 6 is [0, positive infinity], find the value of real number a 6. If the definition field of ax ^ 2-ax + 1 / A under f (x) = root sign is r, find the value range of real number a

If the inequality | X-1 | + | X-2 | < m of X has a solution, then the value range of M is___ 1. If the inequality | X-1 | + | X-2 | < m of X has a solution, then the value range of M is___ 2. Let the image of F (x) be symmetric about y axis and monotone function when x > 0, then the sum of all x satisfying f (x) = f (x + 3 / x + 4) is___ 3. Find the range of function f (x) = x ^ 2-4x + 3 / 2x ^ 2-x-1 4. If 3f (x-1) + 2F (1-x) = 2x, find the analytic expression of F (x) 5. If the range of function f (x) = x ^ 2-4ax + 2A + 6 is [0, positive infinity], find the value of real number a 6. If the definition field of ax ^ 2-ax + 1 / A under f (x) = root sign is r, find the value range of real number a

1, M > 1 (hint: draw a picture)
2, - 8 x = (x + 3) / (x + 4) or - x =
3, (2y-1) x ＾ 2 + (4-y) x - (y + 3) = 0, Δ≥ 0, y is solved
4. Let X-1 = m, replace x, get f (m) = [2 (M + 1) - 2F (- M)] / 3, replace m with - m, f (- M) = Then f (- M) is substituted into the previous one, f (m) is solved by solving the equation, and M is replaced by X, that is OK
5,Δ＝0
6,Δ＝0