Question

Consider the function:
$f\left(x\right)=\left[x\right]+\left|1-x\right|,-1\le x\le 3$ where $\left[x\right]$ is the greatest integer function.
Statement 1: $f$ is not continuous at $x=0,1,2$ and $3$.
Statement 2 : $f(x)=\{\begin{array}{ll}-x,& -1\le x<0\\ 1-x& 0\le x<1\\ 1+x& 1\le x<2\\ 2+x& 2\le x\le 3\end{array}$

• A. Statement 1 is true; Statement 2 is false,
• B. Statement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1.
• C. Statement 1 is true; Statement 2 is true; Statement It is a correct explanation for Statement 1.
• D. Statement 1 is false; Statement 2 is true.

Answer 1

Answer: (A)

Let $f\left(x\right)=\left[x\right]+\left|1-x\right|,-1\le x\le 3$
where $\left[x\right]=$ greatest integer function.
$f$ is not continuous at $x=0,1,2,3$
But in statement-2 $f(x)$ is continuous at $x=3$.
Hence, statement-$1$ is true and $2$ is false.