Question

The domain of the function $\frac{1}{\sqrt{[x{]}^2-5[x]+6}}$ is
(where [.] denotes the greatest integer function)

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

Answer 1

The correct option is C $(-\infty ,2)\cup [4,\infty )$

For the functions to be defined
$[x{]}^2-5[x]+6>0\Rightarrow ([x]-2)([x]-3)>0$
$\Rightarrow \left[x\right]\in (-\infty ,2)\cup (3,\infty )$
$\Rightarrow x\in (-\infty ,2)\cup [4,\infty )$