Question

Function $f\left(x\right)=|x-1|+|x-2|+\cos x$ where $x\in [0,4]$ is not continuous at number of points

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

The correct option is D 0

If $0<x<1$
$f\left(x\right)=-(x-1)-(x-2)cosx$
$=-2x+3+cosx$
If $1<x<2$
$f\left(x\right)=(x-1)-(x-2)+cosx$
$=1+cosx$
If $x>2$
$f\left(x\right)$
$=2x-3+cosx$
${lim}_{x\to 1^{-}}f\left(x\right)=1+cos1$
${lim}_{x\to 1^{+}}f\left(x\right)=1+cos1$
${lim}_{x\to 2^{-}}f\left(x\right)=1+cos2$
${lim}_{x\to 2^{+}}f\left(x\right)=1+cos2$
So it is continous at all points.