$y = \frac{\sqrt{7 - 14x}}{x + 8}$
$\begin{equation*} \begin{cases} 7 - 14x ≥ 0 &\\ x + 8 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 7 ≥ 14x &\\ x ≠ -8 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x ≤ 0,5 &\\ x ≠ -8 & \end{cases} \end{equation*}$
x ∈ (−∞;−8)U(−8;0,5]

$y = \frac{6}{\sqrt{4 - x} - 1}$
$\begin{equation*} \begin{cases} 4 - x ≥ 0 &\\ \sqrt{4 - x} - 1 ≠ 0 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} 4 ≥ x &\\ (\sqrt{4 - x})^2 ≠ 1^2 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x ≤ 4 &\\ 4 - x ≠ 1 & \end{cases} \end{equation*}$
$\begin{equation*} \begin{cases} x ≤ 4 &\\ x ≠ 3 & \end{cases} \end{equation*}$
x ∈ (−∞;3)U(3;4]