Example 1 (1993 National High School League Question) Given $f(x)=a \sin x+b \sqrt[3]{x}+4$ (where $a, b$ are real numbers) and $f\left(\lg _{0} \log _{3} 10\right)=5$, then the value of $f(\lg \lg 3)$ is $(\quad)$.
A. -5
B. 0
C. 3
D. Varies with different values of $a, b$
Solution: Choose C. Reason: Since $f(x)-4=a \sin x+b \sqrt[3]{x}=g(x)$ is an odd function, we have $g(-x)=-g(x)$, which means $f(-4)-4=-[f(x)-4]$, or $f(-x)=-f(x)+8$. Also, $\lg \lg 3=-\lg \lg 310$, thus, $f\left(\lg \lg _{3}\right)=$