$\"\"$

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 $\"\"$ .

$\"\"$ .

$\"\"$ , which is always positive for $\"\"$ so the function $\"\"$ is strictly increasing on its domain.

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

There is no negative terms so the function $\"\"$ is monotonic.

Therefore $\"\"$ is monotonic and it has an inverse function. $\"\"$

Inverse function of $\"\"$ exists because the function $\"\"$ is monotonic.