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Latest revision as of 11:46, 3 June 2024

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 (Problems • Answer Key • Resources)
Preceded by
Problem 11 		Followed by
Problem 13
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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