| \[f(x)=\left\{ \begin{matrix} \left| x \right|+\left[ x \right] & , & -l\le x<l \\ x+\left| x \right| & , & l\le x<2 \\ x+\left[ x \right] & , & 2\le x\le 3 \\ \end{matrix}, \right.\] |
| where [t] denotes the greatest integer less than or equal to t. Then, ? is discontinuous at: |
A) four or more points
B) only one point
C) only two points
D) only three points
Correct Answer: D
Solution :
\[f(x)=\left\{ \begin{matrix} -(x+1) & , & -\le x<0 \\ x & , & 0\le x<l \\ 2x & , & l\le x<2 \\ x+2 & , & 2\le x<3 \\ x+3 & , & x=3 \\ \end{matrix} \right.\] function discontinuous at x = 0,1,3
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