Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

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

Pick one

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 implies that the answer is $\fbox{E}$ . ~ samrocksnature
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