The domain of the function $f(x) = \frac{\sin^{-1}(3 - x)}{\ln(|x| - 2)}$ is

The domain of the real-valued function $f(x) = \frac{\sqrt{\log_{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}}$ is (where $[x]$ denotes the greatest integer function):

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 . . . . . . .

If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$,then the range of $f(x)$ is contained in the interval

The domain and range of $f(x) = \frac{1}{\sqrt{|x| - x^2}}$ are $A$ and $B$ respectively. Then $A \cup B =$

The range of the function $f(x) = \frac{\sqrt{1 - x^2}}{1 + |x|}$ is