The graph of the function is given in Fig 5 4 Example 11 Find all the points of discontinuity of the function f defined by
f (x) = 
2, if
1
0,
if
1
2, if
1
x
x
x
x
x
+
<

=

 −
>

Solution As in the previous example we find that f
is continuous at all real numbers x ≠ 1 The left
hand limit of f at x = 1 is
–
1
1
lim
( )
lim (
2)
1
2
3
x
x
f x
x
→−
=→
+
= +
=
The right hand limit of f at x = 1 is
1
1
lim
( )
lim (
2)
1
2
1
x
x
f x
x
+
+
→
=→
−
= −
= −
Since, the left and right hand limits of f at x = 1
do not coincide, f is not continuous at x = 1