If the domain of the function $f(x) = \log_7(1 - \log_4(x^2 - 9x + 18))$ is $(\alpha, \beta) \cup (\gamma, \delta)$,then $\alpha + \beta + \gamma + \delta$ is equal to

If $[x]^2-5[x]+6=0$,where $[\cdot]$ denotes the greatest integer function,then $x$ belongs to:

Define the real-valued function $f: R - \{0\} \rightarrow R$ defined by $f(x) = \frac{1}{x}$,where $x \in R - \{0\}$. Complete the table given below using this definition. What is the domain and range of this function?

$x$	$-2$	$-1.5$	$-1$	$-0.5$	$0.25$	$0.5$	$1$	$1.5$	$2$
$y = \frac{1}{x}$	....	....	....	....	....	....	....	....	....

Let the range of the function $f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, x \in \mathbb{R}$ be $[a, b]$. If $\alpha$ and $\beta$ are respectively the $A.M.$ and the $G.M.$ of $a$ and $b$,then $\frac{\alpha}{\beta}$ is equal to:

Let $f(x) = \sqrt{\frac{x+1}{x+3}}$ and $g(x) = \sqrt{\frac{2-x}{x+3}}$ be two real-valued functions. Then the domain of $f/g$ is

If the domain of the greatest integer function is the set of real numbers,then the range will be the set of