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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value

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Bunuel
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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   31 May 2018, 11:59
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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. \(f(x)=\sqrt{(x-4)}\)
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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   01 Jun 2018, 00:12
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Calculating \(\frac{1}{2} * f(x)\) for each of the answer options, we get
A. \(f(x)= 2x+2\) -> \(\frac{1}{2} * f(x) = \frac{2(x+1)}{2} = (x+1)\). Now, \(f(\frac{1}{2}*x) = 2*\frac{1}{2}*x + 2 = x + 2\)

B. \(f(x)=13x\) -> \(\frac{1}{2} * f(x) = \frac{13x}{2}\). Now, \(f(\frac{1}{2}*x) = 13*\frac{x}{2}= \frac{13x}{2}\)

We have a match for \(\frac{1}{2} * f(x) = f(\frac{1}{2}*x)\)

Therefore, Option B [f(x) = 13x] is the correct answer.
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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   03 Jun 2018, 18:28
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Bunuel wrote:
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. \(f(x)=\sqrt{(x-4)}\)


We can let x = 2, and we have:

½f(2) = f(1)

Let’s analyze each answer choice:

A) f(x) = 2x + 2

½f(2) = ½(2(2) + 2) = ½(6) = 3

f(1) = 2(1) + 2 = 4

A is not correct.

B) f(x) = 13x

½f(2) = ½(13(2)) = ½(26) = 13

f(1) = 13(1) = 13

B is correct.

Answer: B
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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   04 Jun 2018, 02:38
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Bunuel wrote:
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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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   17 Dec 2019, 06:57
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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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink] New post   27 Nov 2022, 05:22
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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value [#permalink]
27 Nov 2022, 05:22
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