Question

Number of integers in the domain of the function $f(x)=\frac{1}{\sqrt{\left\{x^2\right\}-x^2+3}}$ is
[Note: $\{x\}$ denotes fractional part function of $x$ ]

• A. 5
• B. 4
• C. 3
• D. 0

Answer 1

Answer: (C)

$x^2-\left[x^2\right]=\left\{x^2\right\}$
$\left\{ x ^2\right\}- x ^2=-\left[ x ^2\right] \Rightarrow f ( x )=\frac{1}{\sqrt{3-\left[ x ^2\right]}} $
$0 \leq\left[ x ^2\right]<3$
$0 \leq x ^2< 3 $
$x \in(-\sqrt{3}, \sqrt{3}) \Rightarrow 3 $