2. Given $f(x)=a \sin x+b \sqrt[3]{x}+4(a, b$ 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 the values of $a, b$
(C)
2. 【Analysis and Solution】 $\because f(x)-4$ is an odd function,

thus $f(-x)-4=-(f(x)-4)$,
i.e., $f(-x)=-f(x)+8$, and $\lg \lg 3=-\lg \log _{3} 10$.
$$
\therefore f(\lg \lg 3)=f\left(-\lg \log _{3} 10\right)=-f\left(\lg \log _{3} 10\right)+8=-5+8=3 .
$$