Therefore,
lim
( )
lim
x
c
x
c
f x
→
=→
(x – 2) = c – 2 = f (c)
Thus, f is continuous at all points x > 1 Case 3 If c = 1, then 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 Fig 5