Question

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{[x{]}^2-[x]-6}}$,where $[\cdot ]$ denotes the greatest integer function

• A. $x\in (-\infty ,-1)\cup (4,\infty )$
• B. $x\in (-\infty ,-4)\cup (4,\infty )$
• C. $x\in (-\infty ,-3)\cup (4,\infty )$
• D. $x\in (-\infty ,-2)\cup (4,\infty )$

Answer 1

Answer: (D)

$x\in (-\infty ,-2)\cup (4,\infty )$

Given function is, $f\left(x\right)=\frac{1}{\sqrt{[x{]}^2-[x]-6}}$
For this function to define,$[x{]}^2-[x]-6>0$
$\Rightarrow \left(\right[x]-3)\left(\right[x]+2)>0$
$\Rightarrow \left[x\right]\in (-\infty ,-2)\cup (3,\infty )$
$\Rightarrow x\in (-\infty ,-2)\cup (4,\infty )$