If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then the range of $f$ is:

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 . . . . . . .

Find the range of the following function:
$f(x) = 2 - 3x$,where $x \in R$ and $x > 0$.

The domain of the real valued function $f(x) = \log_{\sqrt{2}}(\sqrt{x^2+x} + \sqrt{x^2-x})$ is

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