3
Rationalised 2023-24
 MATHEMATICS
110
Example 10 Discuss the continuity of the function f defined by
f (x) =
2, if
1
2, if
1
x
x
x
x
+
≤

 −
>

Solution The function f is defined at all points of the real line Case 1 If c < 1, then f(c) = c + 2 Therefore, lim
( )
lim(
2)
2
x
c
x
c
f x
x
c
→
=→
+
=
+
Thus, f is continuous at all real numbers less than 1 Case 2 If c > 1, then f (c) = c – 2