1993 AHSME Problems/Problem 12

Problem

If $f(2x)=\frac{2}{2+x}$ for all $x>0$, then $2f(x)=$

$\text{(A) } \frac{2}{1+x}\quad \text{(B) } \frac{2}{2+x}\quad \text{(C) } \frac{4}{1+x}\quad \text{(D) } \frac{4}{2+x}\quad \text{(E) } \frac{8}{4+x}$

Solution

As $f(2x)=\frac{2}{2+x}$, we have that $f(x)=\frac{2}{2+\frac{x}{2}}$. This also means that $2f(x)=\frac{4}{2+\frac{x}{2}}$ which simplifies to $\fbox{E}$.

~ samrocksnature

~ clarification by Leon

Note: Wait what

See also

1993 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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