$\"\"$

\

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 $\"\"$ .