Mathematics - Functions Question with Solution | TestHub

$f\left(x\right)+g\left(x\right)=\sqrt{x}+\sqrt{1-x},$ domain $\left[0, 1\right]$

$f\left(x\right)-g\left(x\right)=\sqrt{x}-\sqrt{1-x},$ domain $\left[0, 1\right]$

$g\left(x\right)-f\left(x\right)=\sqrt{1-x}-\sqrt{x},$ domain $\left[0, 1\right]$

$\frac{f\left(x\right)}{g\left(x\right)}=\frac{\sqrt{x}}{\sqrt{1-x}},$ domain $[0, 1)$

$\frac{g\left(x\right)}{f\left(x\right)}=\frac{\sqrt{1-x}}{\sqrt{x}},$ domain $(0, 1]$

So, common domain is $\left(0, 1\right)$