List of top Mathematics Questions on types of functions asked in COMEDK UGET

The domain of the function \[ f(x)=\sin^{-1}(\sqrt{x-1}) \] is:
A function \( f \) from the set of natural numbers to integers defined by \[ f(n) = \begin{cases} \frac{n-1}{2}, & \text{when } n \text{ is odd} -\frac{n}{2}, & \text{when } n \text{ is even} \end{cases} \] is
Domain of the function \[ f(x) = \sqrt{\sin^{-1}(2x) + \frac{\pi}{6}} \text{ for real values of } x \]
If a function \( f : [2, \infty) \to \mathbb{R \) is defined by} \[ f(x) = x^2 - 4x + 5 \] then the range of \( f \) is:
If \( f(x) \) satisfies the relation \( 2f(x) + f(1 - x) = x^2 \) for all real \( x \), then \( f(x) \) is: