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

Find the domain and range of the following real function:
$f(x) = \sqrt{9 - x^{2}}$

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$, where $[y]$ denotes the greatest integer not exceeding $y$, then $\{f(x) : |x| < 71\}$ is equal to

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
$(S2): A \cup B = (1, \infty)$

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

The largest interval lying in $\left( -\frac{\pi}{2}, \frac{\pi}{2} \right)$ for which the function $f(x) = 4^{-x^2} + \cos^{-1}\left( \frac{x}{2} - 1 \right) + \log(\cos x)$ is defined is: