Question

The domain of the function $f$ defined as $f\left(x\right)=\frac{1}{{\left[X\right]}^2-3\left[X\right]+2}$ ( where $\left[\right]$ denotes greatest integer function ) is ?

• A. $(-\infty ,-1)\cup (3,\infty )$
• B. $(-\infty ,-3)\cup (-1,\infty )$
• C. $(-\infty ,1)\cup (3,\infty )$
• D. $(-\infty ,1)\cup [3,\alpha )$

Answer 1

The correct option is D $(-\infty ,1)\cup [3,\alpha )$

$\Rightarrow f\left(x\right)=\frac{1}{y^2-3y+2}\{y=[x\left]\right\}$

$=\frac{1}{(y-1)(y-2)}$

As denominator $\ne 0$

$\Rightarrow y\ne 1,2$

$\Rightarrow \left[x\right]\ne 1,2$

$\Rightarrow x\text{/}\in [1,3)$

$\Rightarrow \left(D\right)$.