$\text{ If the functions are defined as }f\left(x\right)=\sqrt{x}\text{ and }g\left(x\right)=\sqrt{1-x},\text{ then what is the common }$

$\text{ domain of the following functions: }f+g,f-g,\frac{f}{g},\frac{g}{f},g-f$

$\text{ The given functions are }f\left(x\right)=\sqrt{x}, g\left(x\right)=\sqrt{1-x}$

$\text{ The domain of the functions and both not equal to zero when }x>0,1-x>0 \Rightarrow$ $x>0, x-1<0$

$\begin{array}{l}\text{ Therefore, the common domain to all functions required is }\\ 0<x<1\end{array}$