TXĐ: \(D=R\)
\(F=\frac{-2\left(x^2+1\right)}{\left(x^2+1\right)\left(x^2+3\right)}=\frac{-2}{x^2+3}\)
\(\left|x+1\right|=3\Rightarrow\left[{}\begin{matrix}x+1=3\\x+1=-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}F=\frac{-2}{2^2+3}=-\frac{2}{7}\\F=\frac{-2}{\left(-4\right)^2+3}=-\frac{2}{19}\end{matrix}\right.\)
\(F=\frac{8}{4x-11}\Leftrightarrow\frac{-2}{x^2+3}=\frac{8}{4x-11}\) (\(x\ne\frac{11}{4}\))
\(\Leftrightarrow4x^2+12=-4x+11\Leftrightarrow4x^2+4x+1=0\Rightarrow x=-\frac{1}{2}\)
\(F\) nhỏ nhất khi \(x^2+3\) nhỏ nhất, mà \(x^2+3\ge3\Rightarrow F\ge\frac{-2}{3}\)
\(\Rightarrow F_{min}=-\frac{2}{3}\) khi \(x=0\)