If the functions are defined as $f(x)=\sqrt{x}$ and $\mathrm{g}(\mathrm{x})=\sqrt{1-\mathrm{x}}$, then what is the common domain of the following functions:
$f+g, f-g, f / g, g / f, g-f$ where
$(f \pm g)(x)=f(\mathrm{x}) \pm \mathrm{g}(\mathrm{x}),(f / \mathrm{g})(\mathrm{x})=\frac{f(\mathrm{x})}{\mathrm{g}(\mathrm{x})}$
Correct Option: , 3
$f(x)+g(x)=\sqrt{x}+\sqrt{1-x}$, domain $[0,1]$
$f(x)-g(x)=\sqrt{x}-\sqrt{1-x}$, domain $[0,1]$
$\mathrm{g}(\mathrm{x})-f(\mathrm{x})=\sqrt{1-\mathrm{x}}-\sqrt{\mathrm{x}}$, domain $[0,1]$
$\frac{f(x)}{g(x)}=\frac{\sqrt{x}}{\sqrt{1-x}}$, domain $[0,1)$
$\frac{g(x)}{f(x)}=\frac{\sqrt{1-x}}{\sqrt{x}}$, domain $(0,1]$
So, common domain is $(0,1)$
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