Question

Let $f:[-1,3]\to R$ be defined as

$f\left(x\right)=\{\begin{array}{c}|x|+\left[x\right],-1\le x<1\\ x+|x|,1\le x<2\\ x+\left[x\right],2\le x\le 3\end{array}$

where $\left[t\right]$ denotes the greatest integer less than or equal to $t$. Then, $f$ is discontinuous at :

• A. only one point
• B. only two points
• C. only three points
• D. four or more points

Answer 1

The correct option is C only three points

$f\left(x\right)=\{\begin{array}{c}-x-1,-1\le x<0\\ x,0\le x<1\\ 2x,1\le x<2\\ x+2,2\le x<3\\ x+3,x=3\end{array}$

Clearly, we can see the function is discontinuous at $x=0,1,3$