Question

The domain of the function f(x) given by $f\left(x\right)=\frac{1}{\sqrt{x+\left|x\right|}}$ is

• A. R
• B. $R^{+}$
• C. $R^{-}$
• D. $R-\{-1\}$

Answer 1

The correct option is B $R^{+}$

Given $f\left(x\right)=\frac{1}{\sqrt{x+\left|x\right|}}\mathrm{If}x>0,\left(x\right|=x\Rightarrow x+\left(x\right|=2x\mathrm{which}\mathrm{is}\mathrm{greater}\mathrm{than}0.\mathrm{If}x\le 0,\left(x\right|=-x\Rightarrow x+\left(x\right|=0f\left(x\right)\mathrm{will}\mathrm{not}\mathrm{be}\mathrm{defined}\mathrm{if}x+\left(x\right|=0\mathrm{Therefore},\mathrm{the}\mathrm{domain}\mathrm{of}f\left(x\right)=R^{+}$