7. 109 If for all $x>0, f(2 x)=\frac{2}{2+x}$, then $2 f(x)$ equals
(A) $\frac{2}{1+x}$.
(B) $\frac{2}{2+x}$.
(C) $\frac{4}{1+x}$.
(D) $\frac{4}{2+x}$.
(E) $\frac{8}{4+x}$.
(44th American High School Mathematics Examination, 1993)
[Solution] $2 f(x)=2 f\left(2 \cdot \frac{x}{2}\right)=2\left[\frac{2}{2+\frac{x}{2}}\right]=\frac{8}{x+4}$. Therefore, the answer is $(E)$.