Domain of the real valued function $f(x) = \frac{x+2}{9-x^{2}}$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - [x] - 6}}$,where $[x]$ is the greatest integer function $\leq x$,is:

Let the sets $A$ and $B$ denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$ where $\lceil x \rceil$ denotes the smallest integer greater than or equal to $x$. Then among the statements
$(S1): A \cap B = (1, \infty) - \mathbb{N}$ and
$(S2): A \cup B = (1, \infty)$

Function $f:(2, \infty) \rightarrow R$ defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is $=$ . . . . . . .

Range of the function $f(x) = 3 + 2^x + 4^x$ is

The domain of the function $f(x) = \sqrt{\log_{10}\left(\frac{5x - x^2}{4}\right)}$ is: