Given f x - x -1- x -1- - Then f x isA- Discontinuous at x-0B- discontinuous at x- 1C- Discontinuous at all integersD- continuous everywhere

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Single Point Continuity

Given f x =| ...

Question

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

Discontinuous at x = 0

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discontinuous at x = ± 1

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Discontinuous at all integers

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continuous everywhere

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Solution

The correct option is D
continuous everywhere

Given function is,

$f (x) = | x - 1 | + | x + 1 |$

for $x < - 1$

$f (x) = 1 - x - x - 1$

$= - 2 x$

for $- 1 < x < 1$

$f (x) = 1 - x + x + 1$

$= 2$

for $x > 1$

$f (x) = x - 1 + x + 1$

$= 2 x$

$∴$ The function can be drawn as below

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

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Given f(x)=|x−1|+|x+1|. Then f(x) is

The correct option is D continuous everywhere Given function is, f(x)=|x−1|+|x+1| for x<−1 f(x)=1−x−x−1 =−2x for −1<x<1 f(x)=1−x+x+1 =2 for x>1 f(x)=x−1+x+1 =2x ∴ The function can be drawn as below From this its clear that the function is not discontinuous at any point.

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