Hence, f
is continuous at all points Example 8 Discuss the continuity of the function f given by f (x) = x3 + x2 – 1 Solution Clearly f is defined at every real number c and its value at c is c3 + c2 – 1 We
also know that
lim
( )
x
c f x
→
 =
3
2
3
2
lim (
1)
1
x
c x
x
c
c
→
+
−
=
+
−
Thus lim
( )
( )
x
c f x
f c
→
=
, and hence f is continuous at every real number