List of top Mathematics Questions on Domain of a Function

Find the domain of \[ p(x)=\sin^{-1}(1-2x^2). \] Hence, find the value(s) of \(x\) for which \[ p(x)=\frac{\pi}{6}. \] Also, write the range of \[ 2p(x)+\frac{\pi}{2}. \]

The domain of \( \sin^{-1}(1 - 2x) \) is :

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 $\sqrt{\frac{x - 7}{9 - x}}$ 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

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