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)

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