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 .