Example 9 Discuss the continuity of the function f defined by f (x) = 1
x , x ≠ 0 Solution Fix any non zero real number c, we have
1
1
lim
( )
lim
x
c
x
c
f x
x
c
→
=→
=
Also, since for c ≠ 0, 
1
f c( )
=c
, we have lim
( )
( )
x
c f x
f c
→
=
 and hence, f is continuous
at every point in the domain of f Thus f is a continuous function Rationalised 2023-24
CONTINUITY AND DIFFERENTIABILITY
109
We take this opportunity to explain the concept of infinity