Solution First note that the function is defined at the given point x = 1 and its value is 5 Then find the limit of the function at x = 1 Clearly
1
1
lim
( )
lim(2
3)
2(1)
3
5
x
x
f x
x
→
=→
+
=
+
=
Thus
lim1
( )
5
(1)
x
f x
f
→
=
=
Hence, f is continuous at x = 1 Example 2 Examine whether the function f given by f(x) = x2 is continuous at x = 0