$\"\"$

Statement: There exists no function $\"\"$ such that $\"\"$ .

There are many functions $\"\"$ , such that $\"\"$ .

All functions which satisfy $\"\"$ also satisfy $\"\"$ .

Consider function $\"\"$ .

Rewrite the function as $\"\"$ .

Find the inverse function.

$\"\"$ .

Interchange the variables $\"image\"$ and $\"image\"$ .

$\"\"$

Substitute $\"\"$ .

The inverse of the function is $\"\"$ .

Therefore, $\"\"$ .

The statement is false.

$\"\"$

The statement is false.