Answer:
The inverse of the function is
.
The domain of the inverse function is ![D:(-\infty,0],\{x|x\in \mathbb{R}\}](https://tex.z-dn.net/?f=D%3A%28-%5Cinfty%2C0%5D%2C%5C%7Bx%7Cx%5Cin%20%5Cmathbb%7BR%7D%5C%7D)
Step-by-step explanation:
Given : Function
where, 
To find : What is the inverse of the function? What is the domain of the inverse?
Solution :
Function 
To find the inverse we interchange the value of x and y,

Now, we get the value of y


As
so x>0

The inverse of the function is
.
The domain of the inverse is the range of the original function.
The range is defined as the set of all possible value of y.
As 
Squaring both side,

Subtract
both side,


The range of the function is ![R:(-\infty,0],\{y|y\in \mathbb{R}\}](https://tex.z-dn.net/?f=R%3A%28-%5Cinfty%2C0%5D%2C%5C%7By%7Cy%5Cin%20%5Cmathbb%7BR%7D%5C%7D)
The domain of the inverse function is ![D:(-\infty,0],\{x|x\in \mathbb{R}\}](https://tex.z-dn.net/?f=D%3A%28-%5Cinfty%2C0%5D%2C%5C%7Bx%7Cx%5Cin%20%5Cmathbb%7BR%7D%5C%7D)