Let and be real-valued functions defined on an interval and suppose that both are…

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f

and

g

be real-valued functions defined on an interval

I

and suppose that both are continuous at

x=c\in I

. (i) State the definition of continuity of a function at a point. (ii) Using only the definition in part (i), explain why

f+g

is continuous at

x=c

. (iii) Give one pair of real functions that are continuous everywhere on

\mathbb R

and show, in one or two sentences, why their difference is continuous at every real number.