Lời giải
* Ta có: \(g\left( x \right) = - 2f\left( {f\left( x \right)} \right) + 3\); \(g'\left( x \right) = - 2.f'(x).f'\left[ {f(x)} \right]\)
* \(f'(x) = 0 \Leftrightarrow \left[ \begin{array}{l}x = 0\\x = a\,\,,\,\,\,\,\,\,\,\,\,\,\,\,a \in (2,\,3)\end{array} \right.\).
* \(g'(x) = 0 \Leftrightarrow \left[ \begin{array}{l}f'(x) = 0\\f'\left[ {f(x)} \right] = 0\,\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 0,\,\,x = a\\f(x) = 0\\f(x) = a\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 0,\,\,x = a\\x = {x_1},\,\,x = {x_4},\,\,x = {x_5}\\x = {x_2},\,\,x = {x_3},\,\,x = {x_6}\end{array} \right.\)
* Gọi \(\alpha = f(a) \in ( - 5,\,\, - 4)\).