$\"\"$

The function is $\"\"$ .

Consider the horizontal line is $\"\"$ .

Graph:

Graph the function for $\"\"$ and the horizontal line is $\"\"$ .

$\"\"$

The horizointal line $\"\"$ touches the graph of the function at only one point.

Hnece the function pass the horizontal line test then the function is an one-to-one function.

The inverse of the function exist.

$\"\"$

The function is $\"\"$ .

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

And the range of the function is $\"\"$ .

Consider $\"\"$ and simplify the function $\"\"$ in terms of $\"\"$ .

$\"\"$

Replace the terms $\"\"$ and $\"\"$ in the above function.

$\"\"$

The function and its inverse are same.

hence the domain and range of the functions are also same.

$\"\"$

Therefore there is not necessary to restrict the domain of the function $\"\"$ .