If the value range of the X-Power of y = e - 1 \ the X-Power of E + 1 is m, what is the function with m as the domain?

If the value range of the X-Power of y = e - 1 \ the X-Power of E + 1 is m, what is the function with m as the domain?

The original meaning of the question should be to let you find the inverse function of the original function. You can see if it is the same as the answer
If so, then this problem is not good
Here is what I ask:
y=(e^x-1)/(e^x+1)=1-2/(e^x+1)
1-y=2/(e^x+1)
e^x+1=2/(1-y)
e^x=2/(1-y)-1=(1+y)/(1-y)
x=ln[(1+y)/(1-y)]
That is, the inverse function is y = ln [(1 + x) / (1-x)]

It is known that the function FX = (x power of a + 1) part (x power of a - 1), a > 0. It is proved that the function is an increasing function in the definition domain; And find the value range of FX Detailed process thank you

（1）
This problem needs to calculate parity first
f(-x)=[a^(-x)-1]/[a^(-x)+1]
=[1-a^x]/[1+a^x]
=-(a^x-1)/(a^x+1)
=-f(x)
Therefore, f (x) is an odd function
F (x) is an odd function, so we only discuss the case when x > 0
① When a > 1, a ^ x is an increasing function
Order: 0 ＜ x1 ＜ x2
Then, f (x1) - f (x2) = [(a ^ x1-1) / (a ^ X1 + 1)] - [(a ^ x2-1) / (a ^ x2 + 1)]
=[(a^x1-1)*(a^x2+1)-(a^x2-1)*(a^x1+1)]/[(a^x1+1)*(a^x2+1)]
The denominator of the above fraction must be > 0
Molecule = [a ^ (x1 + x2) - A ^ x2 + A ^ x1-1] - [a ^ (x1 + x2) - A ^ X1 + A ^ x2-1]
=2(a^x1-a^x2)
Because a ^ x is an increasing function and X1 < x2
So, a ^ X1 < A ^ x2
Therefore, f (x1) - f (x2) < 0
That is, f (x1) < f (x2)
So, f (x) is an increasing function
And f (x) is an odd function on R
So, on R, f (x) is an increasing function
② When 0 < a < 1, similarly, it can be obtained that f (x) is a subtractive function on R
（2）
Find the value range of F (x)
Because 0
f(x)=(a^x-1)/(a^x+1)=1-2/(a^x+1)>1-2/(0+1)=-1,
f(x)=(a^x-1)/(a^x+1)=1-2/(a^x+1)

What is the definition domain of the 1 / X-5 power of function y = 2? What is the range?

The definition field is the meaningful range of the function. In order to make the function meaningful, the denominator cannot be 0, so X-5 ≠ 0, X ≠ 5
As for the value range, you can solve it by drawing.. if you remember correctly, it is (0, + ∞)

What are the definition fields and value fields of function y = (the - x power of 3) - 1? Want process

No matter what value x takes, the function makes sense, so the definition domain of the function is r
From y = 3 ^ (- x) - 1, 3 ^ (- x) = y + 1 > 0, so Y > - 1, so the value range of the function is Y > - 1

If the function y = 22x-2x + 2 + 7, the definition field is [M, n], and the value field is [3, 7], then the maximum value of N + m __

Because y = 22x-2x + 2 + 7 = (2x) 2-4 ⋅ 2x + 7, let t = 2x,
Because m ≤ t ≤ n, 2m ≤ t ≤ 2n
Therefore, the original function is equivalent to y = f (T) = t2-4t + 7 = (T-2) 2 + 3,
Because the value range of the function is [3,7], when t = 2, y = 3
From (T-2) 2 + 3 = 7, t = 0 (rounded) or T = 4
When t = 2, 2x = 2, x = 1. When t = 4, 2x = 4, x = 2
Therefore, the definition domain of the function is [M, 2] (0 ≤ m ≤ 1), so when m = 1 and N = 2, the maximum value of M + n is 3
So the answer is: 3

Variation of exponential function and power function image with X It seems that there is something a between 0 and 1. The closer the image is to the Y axis (x axis), the more detailed it is@_@

Let's start with the exponential function, that is, the form of y = a ^ x (a > 0). If a > 1, the whole image is a curve with low left and high right passing through the fixed point (0,1). Moreover, with the increase of a, the positive half of the X-axis becomes steeper and steeper (that is, it approaches the y-axis faster, that is, it increases faster). At the same time, the secondary half of the x-axis approaches the x-axis faster (generally speaking, it decreases quickly, of course, it will never be less than 0); for the case of a < 0, just contrary to the above, the left is high and the right is low. With the decrease of a, the left becomes steeper and steeper. In fact, you only need to make the image of positive number - a opposite to a symmetrical about the Y axis
Let's look at the power function y = x ^ A, which has no definite form. The function curve will change greatly with the different of A. for example, a = 1 is a straight line, a = 2 is a parabola, a = - 1 is a hyperbola, a = 0.5 is a parabola with a defined opening to the right only in the positive half of the X axis, and so on