Example 13 Discuss the continuity of the function f given by
f (x) = 
,2
if
0
, if
0
x
x
x
x
≥

<

Solution Clearly the function is defined at
every real number Graph of the function is
given in Fig 5 7 By inspection, it seems prudent
to partition the domain of definition of f into
three disjoint subsets of the real line