$\"\"$

The area of the circle with radius $\"\"$ is $\"\"$ .

The radius $\"\"$ is always positive and greater than zero.

The area of the circle appears to be continuous in the interval $\"\"$ .

$\"\"$

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

$\"\"$ .

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

Therefore, the function is one-to-one and is strictly monotonic over the interval.

Inverse exists.

$\"\"$

Find the inverse of the function.

The function is $\"\"$ .

Rewrite the function as $\"\"$ .

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

$\"\"$

Substitute $\"\"$ .

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

$\"\"$

The function has inverse function.

The inverse of area of the circle is $\"\"$ .