Question

If $f\left(x\right)=\left[\right[x\left]\right]-[x-1]$ then which of the following options is CORRECT, (where $[.]$ represents the greatest integer function.)

• A. Discontinuous at $x=0$
• B. Discontinuous at $x=1$
• C. Discontinuous at $x=-1$
• D. Continuous at every where

Answer 1

The correct option is D Continuous at every where

$f\left(x\right)=\left[\right[x\left]\right]-[x-1]=\left[x\right]-\left(\right[x]-1)=1$
$\Rightarrow f\left(x\right)$ is continuous $\forall x\in R$