Page 241 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 2. If a function is continuous then the constant multiple of that function is also continuous.
Figure 8.1

Consider the function f(x) = . We know that x is a constant function. Let ‘a’ be an

arbitrary real number.
=

=

= …(i)

Also f(a) = …(ii)

From (i) and (ii),
= f(a)

f(x) = is continuous at x = a.

As is constant, and x is continuous function at x = a, is also a continuous function at

x = a.
2
3. Consider the function f(x) = x + 2x. We know that the function x and 2x are continuous.
2
Now =
=

=

2
= a + 2a …(i)
2
Also f(a) = a + 2a … (ii)
From (i) and (ii), f(a)

f(x) is continuous at x = a.

234 LOVELY PROFESSIONAL UNIVERSITY