The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - [x] - 2}}$ is,where $[x]$ denotes the greatest integer function.

Find the range of the following function:
$f(x) = x^{2} + 2$,where $x$ is a real number.

The domain of the function $f(x) = \log(\log(\log(...\log(x)...)))$ where the logarithm is applied $n$ times (base $10$) 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 . . . . . . .

The least value of $2^{(x^2 - 3)^3+27}$ is-

Domain of the function $f$,given by $f(x) = \frac{1}{\sqrt{(x - 2)(x - 5)}}$ is