Hence, f is continuous at x = 0 Example 4 Show that the function f given by
f(x) =
3
3, if
0
1,
if
0
x
x
x

+
≠

=

is not continuous at x = 0 Rationalised 2023-24
CONTINUITY AND DIFFERENTIABILITY
107
Solution The function is defined at x = 0 and its value at x = 0 is 1 When x ≠ 0, the
function is given by a polynomial