Question

If $[.]$ denotes GIF. The possible values of $x$ which holds true for the function $\frac{1}{\sqrt{\left(\right[x]-5)}}$ is/are .

• A. $(-\infty ,5)$
• B. $[6,\infty )$
• C. $[5,\infty )$

Answer 1

The correct option is B $[6,\infty )$

Given function: $\frac{1}{\sqrt{\left[x\right]-5}}$

For the function to be defined, $\left[x\right]-5>0$
We know $\left[x\right]>n\iff x\ge n+1,n\in Z$
$\Rightarrow x\ge 5+1$
$\Rightarrow x\in [6,\infty )$