$\"\"$

The function is $\"\"$ and interval is $\"\"$ .

$\"\"$

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

Apply formula : $\"\"$ .

$\"\"$ on $\"\"$ .

The derivative is always positive on $\"\"$ therefore $\"\"$ is increasing and thus has an inverse on this interval.

$\"\"$ is strictly monotonic and it have an inverse function.

$\"\"$

$\"\"$ is strictly monotonic and it have an inverse function.