Cho

A

- Hướng dẫn giải

Đáp án A

Ta có $5^{{\log }_{c}6}=6^{{\log }_{c}5}\iff 5^{{\log }_{c}6}+\left(-6^{{\log }_{c}5}\right)=0$ . Mà 

$f\left(-x\right)=a{\ln }^{2017}\left(\sqrt{x^2+1}-x\right)-bx{\sin }^{2018}x+2$

$$\begin{gathered} a{\ln }^{2017}\left(\frac{1}{\sqrt{x^2+1}+x}\right)-bx{\sin }^{2018}x+2 \\ =-a\ln 2017\left(\sqrt{x^2+1}+x\right)-bx{\sin }^{2018}x+2 \end{gathered}$$

$$\begin{gathered} \Rightarrow f\left(x\right)+f\left(-x\right)=4\Rightarrow f\left(-6^{{\log }_{c}5}\right)+f\left(5^{{\log }_{c}6}\right)=4 \\ \Rightarrow f\left(-6^{{\log }_{c}5}\right)=-2 \end{gathered}$$