The function is  in the interval .

Definition of continuity :

A function  is continuous at , if  then it should satisfy three conditions :

(1)  is defined.

(2)  exists.

(3) .

Condition (1):

 is defined.

If  then the function is .

Therefore .

Condition (2):

 exists.

Left hand limit :

.

Right hand limit :

.

Left hand limit and right hand limit are equal, limit exist.

Condition (3) :

.

 and .

.

The three conditions of the continuity are satisfied, hence the function is continuous.

Therefore, the function is continuous over the interval .

The function  is continuous over interval .