If the solve the problem

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 t. Then, ƒ is discontinuous at:

  1. four or more points

  2. only one point

  3. only two points

  4. only three points 


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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