If f(2x)=(2)/(2+x) for all x>0, then 2f(x)=

1993 AMC 12 Problem 12

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12.

f(2x)=\frac{2}{2+x}

for all

x\gt0,

then

2f(x)=

\frac{2}{1+x}

\frac{2}{2+x}

\frac{4}{1+x}

\frac{4}{2+x}

\frac{8}{4+x}

To obtain

f(x),

replace the given input variable by

\frac{x}{2}

Simplify

2f(x)=2\left(\frac{2}{2+\frac{x}{2}}\right)

Replacing the given

x

\frac{x}{2}

yields

f(x)=\frac{2}{2+\frac{x}{2}}=\frac{4}{4+x}.

Therefore

2f(x)=\frac{8}{4+x}.

Thus the correct answer is E.