2. Given $f(x)=a \sin x+b \sqrt[3]{x}+4\left(a, b\right.$ are real numbers) and $f\left(\lg \log _{3} 10\right)$ $=5$, then the value of $f(\lg \lg 3)$ is
(A) -5 ;
(B) -3 ;
(C) 3 ;
(D) takes different values depending on different values of $a, b$.
2. (C)
$\because f(x)-4$ is an odd function,
thus $f(-x)-4=-(f(x)-4)$,
which means $f(-x)=-f(x)+8$, and $\lg \lg 3=-\lg _{0} \log _{3} 10$.
$$
\begin{array}{l}
\therefore f(\lg \lg 3)=f\left(-\lg _{3} 10\right)=-f\left(\lg _{3} \log _{3} 10\right)+8 \\
=-5+8=3 \text {. } \\
\end{array}
$$