If the domain of the function $f(x) = \cos^{-1}\left(\frac{2-|x|}{4}\right) + (\log_e(3-x))^{-1}$ is $[-\alpha, \beta) \setminus \{\gamma\}$,then $\alpha + \beta + \gamma$ is equal to:

Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2\left(2-6\log_{27}(2x+5)\right)$ be $(\gamma, \delta)$. Then $|7(\alpha+\beta)+4(\gamma+\delta)|$ is equal to . . . . . . .

Let $A = \{9, 10, 11, 12, 13\}$ and let $f: A \rightarrow N$ be defined by $f(n) = \text{the highest prime factor of } n$. Find the range of $f$.

The set of values of $\alpha$ such that $f: R \rightarrow [0, \frac{\pi}{2})$ defined by $f(x) = \tan^{-1}(x^2 + x + \alpha^2)$ is onto is

The domain of the function $f(x) = \sqrt{x-1} + \sqrt{6-x}$ is

Range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is