Question

Domain of the function $f\left(x\right)=\frac{1}{\sqrt{x-\left|x\right|}}$ is

• A. $(0,\infty )$
• B. $(\infty ,0)$
• C. $\varphi$
• D. None of these

Answer 1

Answer: (C)

$\varphi$

We have $x-|x|=0,\forall x\in R^{+}\cup \left\{0\right\}$ and

$=-2|x|,\forall x\in R^{-}$.

So, $\sqrt{x-|x|}=0$ $,\forall x\in R^{+}\cup \left\{0\right\}$

$=$ undefined $,\forall x\in R^{-}$.

So, $f\left(x\right)$ is not defined any $x\in R$.

So, domain is $\varphi$.