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Question

Given f(x)=|x1|+|x+1|. Then f(x) is

A

Discontinuous at x = 0

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B

discontinuous at x = ± 1

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C

Discontinuous at all integers

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D

continuous everywhere

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Solution

The correct option is D

continuous everywhere


Given function is,

f(x)=|x1|+|x+1|

for x<1

f(x)=1xx1

=2x

for 1<x<1

f(x)=1x+x+1

=2

for x>1

f(x)=x1+x+1

=2x

The function can be drawn as below

From this its clear that the function is not discontinuous at any point.


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