\(a,\sqrt{\dfrac{2}{9-x}}\) có nghĩa khi \(\left\{{}\begin{matrix}\dfrac{2}{9-x}\ge0\\9-x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}9-x>0\\x\ne9\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x< 9\\x\ne9\end{matrix}\right.\) \(\Leftrightarrow x< 9\)
\(b,\sqrt{x^2+2x+1}\) có nghĩa khi \(x^2+2x+1\ge0\) \(\Leftrightarrow\left(x+1\right)^2\ge0\forall x\)
\(\Rightarrow\sqrt{x^2+2x+1}\) được xác định \(\forall x\)
\(c,\sqrt{9-x^2}=\sqrt{\left(3-x\right)\left(3+x\right)}\) có nghĩa khi \(\left\{{}\begin{matrix}3-x\ge0\\3+x\ge0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\le3\\x\ge-3\end{matrix}\right.\)
\(d,\sqrt{\dfrac{1}{x^2-4}}=\sqrt{\dfrac{1}{\left(x-2\right)\left(x+2\right)}}\) có nghĩa khi \(\left\{{}\begin{matrix}\dfrac{1}{\left(x-2\right)\left(x+2\right)}\ge0\\\left(x-2\right)\left(x+2\right)\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-2\right)\left(x+2\right)>0\\\left(x-2\right)\left(x+2\right)\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>\pm2\\x\ne\pm2\end{matrix}\right.\) \(\Leftrightarrow x>2\)
\(e,\dfrac{1}{\sqrt{x}+1}+\dfrac{\sqrt{x}}{\sqrt{x}-3}\) có nghĩa khi \(\left\{{}\begin{matrix}\sqrt{x}\ge0\\\sqrt{x}+1>0\\\sqrt{x}-3>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x>9\end{matrix}\right.\)
