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Bunuel
Given \(\frac{1}{2} f(x)= f(\frac{1}{2}*x)\), which of the following is true for all values of f(x)?


A. \(f(x)= 2x+2\)

B. \(f(x)=13x\)

C. \(f(x)=x^2\)

D. \(f(x)=x-10\)

E. \(f(x)=\sqrt{(x-4)}\)

Re-writing the given function as f(x)=2f(\(\frac{x}{2}\))

Let's check the validity of the given answer choices.

A. 2f(\(\frac{x}{2}\))=2((\(\frac{x}{2}\))+2)=\({x+4}\neq{f(x)}\)
B. 2f(\(\frac{x}{2}\))=\(2(13*\frac{x}{2})\)=13x=f(x)

hence option(B) is the correct answer.
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This took a little bit of thinking to solve efficiently.

There are 2 ways to solve this.

1) First, is explained by capable friends by substituting value of x by a number say 2.
2) Look closely and you will notice that f((1/2)*x) will effect all x in OA but not the other values.
Except B, all other options have values other than just the variable.

So choose B
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Hello from the GMAT Club BumpBot!

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