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 Hence
x = 1 is the only point of discontinuity of f The
graph of the function is given in the Fig 5 5