)
Since lim
( )
( )
x
c f x
f c
→
=
, f is continuous at all positive real numbers 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