Page 230 - DMTH201_Basic Mathematics-1
P. 230
Unit 8: Continuity
8.1.3 Continuity at an End Point Notes
Example: Show that is continuous from the right at x = 0.
8.1.4 Continuity on an Interval
A function f is said to be continuous on an open interval (a, b) provided that f is continuous
at every value in the interval.
A function f is said to be continuous on a closed interval [a, b] provided that f is continuous
from the right at x = a, continuous from the left at x = b, and continuous at every value in
the open interval (a, b).
8.1.5 Properties of Continuous Functions
If the functions f and g are continuous at x = c, then each of the following functions is also
continuous at x = c:
The sum function f g
The difference function f – g
The product function fg
The quotient function f/g, g(c) 0
8.1.6 Properties of Composite Functions
If the function f is continuous at x = c and the function g is continuous at x = f(c), then the
composite function g o f is continuous at x = c.
Example: Show that is continuous at x = 2.
Solution:
3
f is continuous at x = 2 and f(2) = 2 – 3 ∙ 22 + 2 + 7 = 5
g is continuous at 5 since
Therefore, g o f(x) is also continuous at x = 2.
LOVELY PROFESSIONAL UNIVERSITY 223
