List of top Mathematics Questions on Domain of a Function asked in KEAM

Let \[ f(x)=\sqrt{7-x} \] and \[ g(x)=\sqrt{x-5}. \] Then the domain of the function \[ h(x)=f(x)g(x) \] 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

The domain of the function $f(x)=\sqrt{x^{2}+2x-15}$ is ________.