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algebra intermediate

Problem

If

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

for all

x > 0

, then

2 f (x) =

(A)

\frac{2}{1 + x}

(B)

\frac{2}{2 + x}

(C)

\frac{4}{1 + x}

(D)

\frac{4}{2 + x}

(E)

\frac{8}{4 + x}

Solution

As

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

, we have that

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

. This also means that

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

which simplifies to

\frac{8}{4 + x}

. Note: Wait what

Final answer

E