(ii)
As a special case of (4) above, if f is the constant function f (x) = λ, then the
function g
λ  defined by 
( )
( )
gx
g x
λ
λ
=
is also continuous wherever g(x) ≠ 0 In
particular, the continuity of g implies continuity of 1
g The above theorem can be exploited to generate many continuous functions They
also aid in deciding if certain functions are continuous or not