Given the function f (x) = (MX-1) / (MX + 1) (M > 0, and M is not equal to 1), find the domain of definition of the function F (x) = (x power of m-1) / (x power of M + 1)

Given the function f (x) = (MX-1) / (MX + 1) (M > 0, and M is not equal to 1), find the domain of definition of the function F (x) = (x power of m-1) / (x power of M + 1)

From F (x) = (x power of m-1) / (x power of M + 1)
The domain of knowledge function is r
The solution of the range t = m ^ x
Then t > 0
So the original function becomes
y=（t-1）/(t+1)
=（t+1-2）/(t+1)
=1-2/(t+1)
From t > 0
That is t + 1 > 1
That is, 0 ＜ 1 / (T + 1) ＜ 1
That is, 0 ＜ 2 / (T + 1) ＜ 2
That is - 2 ＜ - 2 / (T + 1) ＜ 0
That is - 1 ＜ 1-2 / (T + 1) ＜ 1
That is - 1 < y < 1
So the range of the function is (- 1,1)

Given that the definition field of function f (x) = √ (m-1) x square + 2 (m-1) x + 3 is real number set R, the value range of real number m is obtained

A real number in the definition field has a real root, Delta (the mathematical symbol is triangle) > 0. Delta is the square of 2 (m-1) - 4 * 3 * (m-1) > 0, and then solve the inequality. Colleagues note that when m = 1, the function is f (x) = 3, which is a constant function and also a representation of real root. The answer is m > 4 or m