NDA 2021 Maths · Mathematics · Continuity and Differentiability · medium

The sum of two continuous functions is continuous. 2. The product of two discontinuous functions is always discontinuous.

Single correct option

Which of the statements is/are correct? 1. The sum of two continuous functions is continuous. 2. The product of two discontinuous functions is always discontinuous.

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

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Answer: (A) 1 only

Statement 1 follows from the algebra of limits and is true. Statement 2 is false: take

f(x)=g(x)=1

for

x\ge0

and

-1

for

x<0

; both are discontinuous at

0

but

fg=1

is continuous everywhere.

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