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

Consider the following lists.

$A$. $f(x)=\frac{|x+2|}{x+2}, x \neq-2$	$1$. $[\frac{1}{3}, 1]$
$B$. $g(x)=|[x]|, x \in R$	$2$. $Z$
$C$. $h(x)=|x-[x]|, x \in R$	$3$. $W$
$D$. $f(x)=\frac{1}{2-\sin 3x}, x \in R$	$4$. $[0, 1)$
	$5$. $\{-1, 1\}$

If $f:[2, \infty) \rightarrow B$ defined by $f(x)=x^2-4x+5$ is a bijection, then $B$ is equal to

For the function $f(x) = \left[ \frac{1}{[x]} \right]$, where $[x]$ denotes the greatest integer less than or equal to $x$, which of the following statements is true?

Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2\left(2-6\log_{27}(2x+5)\right)$ be $(\gamma, \delta)$. Then $|7(\alpha+\beta)+4(\gamma+\delta)|$ is equal to . . . . . . .

The domain of the real-valued function $f(x) = \sqrt{\frac{2x^2 - 7x + 5}{3x^2 - 5x - 2}}$ is