$\"\"$

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

$\"\"$

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

$\"\"$

Apply formula: $\"\"$ .

$\"\"$ .

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

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

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

$\"\"$

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