Cho hàm số

B

- Hướng dẫn giải

Đáp án B

Ta có $g\left(x\right)=f\left(x^2-1\right)\Rightarrow g\text{'}\left(x\right)=2x.f\text{'}\left(x^2-1\right);\forall x\in ℝ$ 

Khi đó

$$\begin{gathered} g\text{'}\left(x\right)<0\iff 2x.f\text{'}\left(x^2-1\right)<0\iff \left[\begin{array}{l}\left\{\begin{array}{l}x>0\\ f\text{'}\left(x^2-1\right)<0\end{array}\right.\\ \left\{\begin{array}{l}x<0\\ f\text{'}\left(x^2-1\right)>0\end{array}\right.\end{array}\right. \\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}x>0\\ x^2-1\in \left(-\infty ;-1\right)\cup \left(2;+\infty \right)\end{array}\right.\\ \left\{\begin{array}{l}x<0\\ x^2-1\in \left(1;2\right)\end{array}\right.\end{array}\right. \end{gathered}$$ 

Suy ra hàm số nghịch biến trên khoảng $\left(-\sqrt{3};-\sqrt{2}\right)$ và $\left(\sqrt{3};+\infty \right)$