AHSME 1993 Problem 12

If $f(2x)=\frac{2}{2+x}$ for all $x>0$, then $2f(x)=$ $\text{(A) } \frac{2}{1+x} \text{(B) } \frac{2}{2+x} \text{(C) } \frac{4}{1+x} \text{(D) } \frac{4}{2+x} \text{(E) } \frac{8}{4+x}$