7.106 Given $f(x)=a \sin x+b \sqrt[3]{x}+4$ (where $a, b$ are real numbers) and $f\left(\lg _{\left.\log _{3} 10\right)} 10\right)$. Then the value of $f(\operatorname{lglg} 3)$ is
(A) -5.
(B) -3.
(C) 3.
(D) It takes different values depending on the values of $a, b$.
(China High School Mathematics League, 1993)
[Solution 1] $\because f(x)-4$ is an odd function, hence $f(-x)-4=-(f(x)-4)$.
That is, $f(-x)=-f(x)+8$, and $\lg \lg 3=-\lg _{2} \operatorname{gog}_{3} 10$.
$$
\begin{array}{l}
=-5+8=3 \text {. } \\
\end{array}
$$

Therefore, the answer is $(C)$.

Thus,
$$
f(x)=\sqrt[3]{\frac{x}{\lg _{3} \log _{3} 10}}+4 \text {, }
$$

So $f(\lg \lg 3)=\sqrt[3]{\frac{\lg \lg 3}{\lg \log _{3} 10}}+4=-1+4=3$, hence we can rule out $(A),(B)$.
Similarly, taking $b=0$, we still get $f(\lg \lg 3)=3$. Therefore, the answer is $(C)$.