Question

The interval in which the relation $|x|=\left\{x\right\}>\left[x\right]$ holds true, is
(Here, $[.]$ and $\{.\}$ represent the greatest integer function and the fractional part function, respectively.)

• A. $[-1,0]$
• B. $[-1,0)$
• C. $(0,1)$
• D. $[0,1)$

Answer 1

The correct option is C $(0,1)$

We know $0\le \left\{x\right\}<1$
Clearly, in $(0,1),$ we have $|x|=\left\{x\right\}>0$
Also, in $(0,1),$ we have $\left[x\right]=0$
$\therefore |x|=\left\{x\right\}>\left[x\right]$ holds true in the interval $(0,1)$