The function is .

A function has an inverse if and only if no horizontal line intersects its graph of the function in at most one point.

The Domain of is .

Observe the graph,

The horizontal line intersects the function more than once, the function is not an one-to-one.

Therefore the inverse of the function doesnot exist.

To find the inverse of the function, restrict the domain of the function such that it is one to one function.

Restricted Domain of is or .

The horizontal line intersects the function at one point.

The function passes the horizontal line test, the function is an one-to-one in the intervals or .

Hence the inverse of the function exist in the interval or .

.

Case 1:

in the domain is .

To find the inverse of the function, consider and solve in terms of .

Now interchange and .

Replace .

The inverse of is  in the domain.

Case 2:

in the domain is

To find the inverse of the function, consider and solve in terms of .

Now interchange and .

The inverse of is    in the domain.

The inverse of is  in the domain.

The inverse of is   in the domain.