Question:
Let $f:[-1,3] \rightarrow \mathrm{R}$ be defined as
$f(x)=\left\{\begin{array}{cc}|x|+[x] & , \quad-1 \leq x<1 \\ x+|x| & , \quad 1 \leq x<2 \\ x+[x] & , \quad 2 \leq x \leq 3\end{array}\right.$
where [t] denotes the greatest integer less than or equal to $\mathrm{t}$. Then, $f$ is discontinuous at:
Correct Option: , 4
Solution:
$f(x)=\left\{\begin{array}{ccc}-(x+1) & , & -1 \leq x<0 \\ x & , & 0 \leq x<1 \\ 2 x & , & 1 \leq x<2 \\ x+2 & , & 2 \leq x<3 \\ x+3 & , & x=3\end{array}\right.$
function discontinuous at $x=0,1,3$
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