List of top Mathematics Questions on Domain of a Function

The domain of the function $\sqrt{\frac{x - 7}{9 - x}}$ is

The domain of the function $f(x)=\sqrt{\frac{x+1}{2-x}}$ is

The domain of the function $f(x)=\sin^{-1}(\sqrt{2-x})$ is

If \(f(x)=\sqrt{2-x^2}\) and \(g(x)=\log(1-x)\) are two real valued functions, then the domain of the function \((f+g)(x)\) is