2. Given $f(x)=a \sin x+b \sqrt[3]{x}+4(a, b$ are real numbers $), f\left(\lg \log _{3} 10\right)=5$, then the value of $f(\lg \lg 3)$ is
A. -5
B. -3
C. 3
D. varies with different values of $a, b$
Let $g(x)=a \sin x+b \sqrt[3]{x}$, then $g(x)$ is an odd function and $g\left(\lg \log _{3} 10\right)=1$.
Also, $\lg \log _{3} 10=\lg \left(\frac{1}{\lg 3}\right)=-\lg \lg 3$
$\Rightarrow f(\lg \lg 3)=g(\lg \lg 3)+4=-g\left(\lg \log _{3} 10\right)+4=3$, so the answer is $C$.