# Why the function is discontinuous at a=1 given #f(x)= 1-x^2# if x < 1 and #f(x)= 1/x# if #x >= 1#?

##### 1 Answer

The limit as

#### Explanation:

There are three requirements for a function

(i)

(ii)

(iii)

**PART 1** We will check if

**PART 2** We will check if

Since the right-hand limit and the left-hand limit are not equal, then the limit as

**The second requirement is not true, therefore the function is discontinuous.**