If the domain of the function $f(x) = \sqrt{\ln(m\sin x + 4)}$ is $R$,then the number of possible integral values of $m$ is:

The domain of the function $f(x) = \frac{\cot^{-1} x}{\sqrt{x^2 - [x^2]}}$,where $[x]$ denotes the greatest integer not greater than $x$,is :

If the function $f: R - \{ 1, - 1\} \to A$ defined by $f(x) = \frac{x^2}{1 - x^2}$ is surjective,then $A$ is equal to

Let the domains of the functions $f(x) = \log_4 \log_3 \log_7(8 - \log_2(x^2 + 4x + 5))$ and $g(x) = \sin^{-1}(\frac{7x + 10}{x - 2})$ be $(\alpha, \beta)$ and $[\gamma, \delta]$,respectively. Then $\alpha^2 + \beta^2 + \gamma^2 + \delta^2$ is equal to:

The range of the function $f(x)=-\sqrt{5-6x-x^2}$ is

Let $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then, the range of $f$ is