What is the range of values for $\frac{x}{x^2 + 4}$ for all real values of $x$?

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 $[x]$ represents the greatest integer $\leq x$ and $[\alpha, \beta]$ is the set of all real values of $x$ for which the real function $f(x)=\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{[x]+2}}$ is defined, then $f^2(\alpha+1)+5 f^2(\beta)=$

The domain of the definition of the function $y(x)$ given by the equation $2^x+2^y=2$ is

If the domain of the function $f(x) = \frac{[x]}{1+x^2}$,where $[x]$ is the greatest integer $\leq x$,is $(2, 6)$,then its range is

The domain of definition of the function $f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x)$ is