Question

Domain of the function $f\left(x\right)=\sqrt{\left[x\right]-x}+\frac{1}{\sqrt{25-x^2}}$ contains the following subset(s), where $[.]$ represents greatest integer function

• A. $\{0,2,4\}$
• B. $\{-2,3,5\}$
• C. $\{-4,-2,1\}$
• D. $\{-3,0,3\}$

Answer 1

Answer: (A), (C), (D)

$\{-3,0,3\}$

Given, $f\left(x\right)=\sqrt{\left[x\right]-x}+\frac{1}{\sqrt{25-x^2}}$

$f\left(x\right)$ is defined when
$\left[x\right]-x\ge 0$ and $25-x^2>0$
$\Rightarrow \left[x\right]-x=0$ and $x^2-25<0$
$\Rightarrow x\in Z$ and $x\in (-5,5)$
$\therefore x\in \{-4,-3,-2,-1,0,1,2,3,4\}$