The range of values of the function $f(x) = \frac{1}{2 - 3\sin x}$ is

The range of $f(x) = \cos[x]$ for $-\frac{\pi}{4} < x < \frac{\pi}{4}$ (where $[.]$ represents the greatest integer function less than or equal to $x$) is

The set of all real values of $x$ such that $f(x) = \sqrt{\frac{[x]-1}{[x]^2-[x]-6}}$ is a real-valued function is

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 domain of the function $f(x) = \sin^{-1}[2x^2 - 3] + \log_2(\log_{1/2}(x^2 - 5x + 5))$,where $[t]$ is the greatest integer function,is:

For the function $f(x) = (1 + \frac{1}{x})^x$,the domain of $f(x)$ is: