The range of the function $f(x) = \sqrt{9 - x^2}$ is

The set of all values of $x$ and the set of all values of $a$ for which the real-valued function $f(x) = \sqrt{\log_a(x - [x])}$ is defined are respectively:

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 real-valued function $f(x) = \frac{\operatorname{cosec}^{-1} x}{\sqrt{x - [x]}}$,where $[x]$ denotes the greatest integer less than or equal to $x$,is defined for all $x$ belonging to:

The range of the function $f(x) = (\sin x)^{\sin x}$ defined on $(0, \pi)$ is

The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well-defined function is