Question

Graph the function $f\left(x\right)=\frac{1}{\sqrt{\left[x\right]-x}}$ and also, determine the domain of $f\left(x\right)$.

• A. $(-\infty ,\infty )$
• B. $\left\{0\right\}$
• C. $\varphi$
• D. $\left\{1\right\}$

Answer 1

Answer: (C)

$\varphi$

$f\left(x\right)=\frac{1}{\sqrt{\left[x\right]-x}}$

For the function to be defined numerator must not be equal to zero and there must be a positive value inside the square root.

$\Rightarrow \left[x\right]-x>0\Rightarrow \left[x\right]>x$

But we know $\left[x\right]\le x$ holds always true.

So domain of the function is null set.

Option $C$ is correct.