If the functions are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the followi…

If the functions are defined as \(f(x)=\sqrt{x}\) and \(g(x)=\sqrt{1-x}\), then what is the common domain of the following functions:
\(f+g,f-g,\frac{f}{g},\frac{g}{f},g-f\) where \((f\pm g)(x)=f(x)\pm g(x)\), \((\frac{f}{g})(x)=\frac{f(x)}{g(x)}\)

[JEE Main 2021, 18 Mar (Shift 1)]