The function .

Theorem :

Any root function is continuous at every number on its domain.

Consider and .

The domain of the root function is and it is continuous in its domain.

The domain of rational function is and it is continuous in its domain.

Domain :

All possible values of is the domain of the function.

The function under the root should not be negative.

Case 1:

If the two factors are positive then the statement holds true.

and

The domain of the function is .

Case 2:

If the two factors are negative then the statement holds true.

and

The domain of the function is . 

The function is continuous at every number in its domain.

Domain of the function is .

Domain of the function is .