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 Therefore,
lim
( )
lim
x
c
x
c
f x
→
=→
(x – 2) = c – 2 = f (c)
Thus, f is continuous at all points x > 1