The domain of $f(x) = [\sin x] \cos \left( \frac{\pi}{[x - 1]} \right)$ is (where $[.]$ denotes the Greatest Integer Function $G.I.F.$).

The domain of the function $f(x) = \log_{3+x}(x^2 - 1)$ is

Let $f: R \rightarrow R$ be defined by $f(x) = \frac{1}{x}$ for all $x \in R$. Then $f$ is:

If the functions are defined as $f(x) = \sqrt{x}$ and $g(x) = \sqrt{1-x}$,then what is the common domain of the following functions: $f+g, f-g, f/g, g/f, g-f$ where $(f \pm g)(x) = f(x) \pm g(x)$ and $(f/g)(x) = \frac{f(x)}{g(x)}$?

The domain of the function $f: R \rightarrow R$ defined by $f(x) = \sqrt{x^{2}-7x+12}$ is

Find the domain of the function $f(x) = \frac{1}{\sqrt{(x + 1)(e^x - 1)(x - 4)(x + 5)(x - 6)}}$.