Cho hàm số 

C

- Hướng dẫn giải

Đáp án C

Ta có

 $\begin{array}{l}y\text{'}={\left(\frac{f\left(x\right)+5}{f^2\left(x\right)+1}\right)}^{\text{'}}\\ =\frac{f\text{'}\left(x\right)\left[f^2\left(x\right)+1\right]-\left[f\left(x\right)+5\right].2f\left(x\right).f\text{'}\left(x\right)}{{\left[f^2\left(x\right)+1\right]}^2}\end{array}$

$\Rightarrow y\text{'}=\frac{f\text{'}\left(x\right).\left[-f^2\left(x\right)-10f\left(x\right)+1\right]}{{\left[f^2\left(x\right)+1\right]}^2}$

Do  hai hàm số cùng đống biến trên $ℝ$ nên 

$\left\{\begin{array}{l}\frac{f\text{'}\left(x\right).\left[-f^2\left(x\right)-10f\left(x\right)+1\right]}{{\left[f^2\left(x\right)+1\right]}^2}\\ f\left(x\right)\ge 0\end{array}\right.$

$\begin{array}{l}\iff -f^2\left(x\right)-10f\left(x\right)+1\ge 0\\ \iff -5-\sqrt{26}\le f\left(x\right)\le -5+\sqrt{26}\end{array}$.