Hence,
lim0
( )
x
f x
→
 =
3
3
0
lim (
3)
0
3
3
x
x
→
+
=
+
=
Since the limit of f at x = 0 does not coincide with f(0), the function is not continuous
at x = 0 It may be noted that x = 0 is the only point of discontinuity for this function Example 5 Check the points where the constant function f(x) = k is continuous Solution The function is defined at all real numbers and by definition, its value at any
real number equals k