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 my Leon Note: Wait what

1993 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1993 AHSME Problems/Problem 12

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