Step 1 :  

Definition of limit :

if and only if and .

Step 2 :

Observe the graph of the function :

As x approaches to 2 from the left side, the value of   tends to 4.

As x approaches to 2 from the right side, the value of   tends to 4.

So we conclude that, .    (From the definition of limit)

Step 3 : 

The fact that has no bearing on the existance or the value of the limit as x  approaches to 2.

For this instance the function was defined as

The limit would be the same. 

Solution : 

 The function