The domain of the function $f(x) = \sin^{-1}\left[\log_4\left(\frac{x}{4}\right)\right] + \sqrt{17x - x^2 - 16}$ is

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

If $x$ is real,then the range of $\frac{x^2+2x+1}{x^2+2x+7}$ is

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ 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 . . . . . . .