$\"\"$

The function is $\"\"$ .

Find an equation for the inverse function.

Let $\"\"$ and solve for $\"\"$ in terms of $\"\"$ .

Let $\"\"$ .

$\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$ .

$\"\"$

The function $\"\"$ is $\"\"$ which can be neither positive or negative depending on the value of $\"\"$ .

The domain of $\"\"$ is $\"\"$ .

Since there is negative terms depending on the value of $\"\"$ , the function $\"\"$ is not monotonic.

$\"\"$ is not a monotonic and it doesnot have an inverse function.

$\"\"$

Inverse function of $\"\"$ does not exist because the function $\"\"$ is not a monotonic.