A function from into itself is continuous at a point if and only if

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A function

f

from

\mathbb{R}

into itself is continuous at a point

a\in\mathbb{R}

if and only if, for each

\epsilon>0

, there exists

\delta>0

such that: (a)

|f(x)-f(a)|<\epsilon\Rightarrow|x-a|<\delta

(b)

|f(x)-f(a)|>\epsilon\Rightarrow|x-a|>\delta

(c)

|x-a|>\delta\Rightarrow|f(x)-f(a)|>\epsilon

(d)

|x-a|<\delta\Rightarrow|f(x)-f(a)|<\epsilon