`7xsqrt{(36+9x)/(-x^2-11)}`
ĐKXĐ : \(\left\{ \begin{array}{l}\dfrac{36+9x}{-x^2-11}\ge0\\-x^2-11\ne0\end{array} \right.\)
`(36+9x)/(-x^2-11) \ge 0`
`⇔`\(\left[ \begin{array}{l}\begin{cases}36+9x\ge0\\-x^2-11>0\end{cases}\\\begin{cases}36+9x\le0\\-x^2-11<0\end{cases}\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}\begin{cases}x\ge-4\\x\in\emptyset\end{cases}\\\begin{cases}x\le-4\\x\in\mathbb{R}\end{cases}\end{array} \right.\)
`⇒ x \le -4`
`-x^2 - 11 \ne 0`
`⇔ -x^2 \ne 11`
`⇔ x^2 \ne -11`
`⇔ |x| \ne sqrt{-11}`
`(`loại `|x| \ge 0 ∀x)`
`-> x ne \emptyset`
`⇒`\(\left\{ \begin{array}{l}x\le-4\\x\ne\emptyset\end{array} \right.\)