$\"\"$

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

Consider $\"\"$ .

$\"\"$

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

$\"\"$

$\"\"$ is always negative in $\"\"$ .

$\"\"$ is decreasing on $\"\"$ .

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

$\"\"$

$\"\"$ is decreasing on $\"\"$ .

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