1. Tardigrade
  2. Question
  3. Mathematics
  4. Let f: [-1,3] arrow R be defined as f(x) = begincases |x|+[x] , &-1 le x < 1 x +|x | , 1 le x < 2 x+|x| ,& 2 le x le 3' endcases where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at:

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Q. Let $f : \left[-1,3\right] \rightarrow R$ be defined as
$f(x) = \begin{cases} |x|+[x] , &-1 \le x < 1 \\ x +|x | , & 1 \le x < 2 \\ x+|x| ,& 2\le x \le 3' \end{cases} $
where [t] denotes the greatest integer less than or equal to t. Then, $ f $ is discontinuous at:

JEE MainJEE Main 2019Continuity and Differentiability

Solution:

$f(x) = \displaystyle\begin{cases}\end{cases} $ $ \begin{matrix}-\left(x+1\right)&,&-1\le x<0\\ x&,&0\le x\le1\\ 2x&,&1\le x<2\\ x+2&,&2\le x<3\\ x+3&,&x=3\end{matrix} \quad$
function discontinuous at $x = 0,1 ,3$