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# If 1/2*f(x) = f(x/2), which of the following is true for all values

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
If 1/2*f(x) = f(x/2), which of the following is true for all values  [#permalink]

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31 Jul 2018, 00:14
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35% (medium)

Question Stats:

66% (01:30) correct 34% (01:36) wrong based on 85 sessions

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If $$\frac{1}{2}f(x) = f(\frac{x}{2})$$, 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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Math Expert
Joined: 02 Aug 2009
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If 1/2*f(x) = f(x/2), which of the following is true for all values  [#permalink]

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31 Jul 2018, 01:45
Bunuel wrote:
If $$\frac{1}{2}f(x) = f(\frac{x}{2})$$, 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) $$f(x) =\sqrt{x-4}$$

the function should tell us that whenever we are adding any numeric value to x, say 10,2,1 etc, there will be no effect on f(x/2) but 1/2 f(x) will half it..
for example $$f(x) = 2x+2$$ so $$\frac{1}{2} f(x) = \frac{(2x+2)}{2}=x+1$$.......... BUT $$f(\frac{x}{2}) = \frac{2*x}{2}+2=x+2$$
therefore eliminate all those - A,D,E

whenever the equation is not linear, f(x/2) will change as the 2 in denominator will change by that power
for example $$f(x) = x^2...........\frac{1}{2}f(x)=\frac{x^2}{2}$$ but $$f(\frac{x}{2})=\frac{x^2}{4}$$
eliminate C

if you understand teh above points, you will look for a linear x with no addition/subtraction of numeric value
such as 13x, 25x and so on

B
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Re: If 1/2*f(x) = f(x/2), which of the following is true for all values  [#permalink]

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10 Aug 2018, 02:28
chetan2u wrote:
Bunuel wrote:
If $$\frac{1}{2}f(x) = f(\frac{x}{2})$$, 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) $$f(x) =\sqrt{x-4}$$

the function should tell us that whenever we are adding any numeric value to x, say 10,2,1 etc, there will be no effect on f(x/2) but 1/2 f(x) will half it..
for example $$f(x) = 2x+2$$ so $$\frac{1}{2} f(x) = \frac{(2x+2)}{2}=x+1$$.......... BUT $$f(\frac{x}{2}) = \frac{2*x}{2}+2=x+2$$
therefore eliminate all those - A,D,E

whenever the equation is not linear, f(x/2) will change as the 2 in denominator will change by that power
for example $$f(x) = x^2...........\frac{1}{2}f(x)=\frac{x^2}{2}$$ but $$f(\frac{x}{2})=\frac{x^2}{4}$$
eliminate C

if you understand teh above points, you will look for a linear x with no addition/subtraction of numeric value
such as 13x, 25x and so on

B

Thanks for the explanation but I can not understand why f(x/2) plugged in with answer choice A is ((2x)/2) +2 instead of (2x+2)/2

I somehow understand that we can't replace the x with the complete f(x) in A but I don't understand why it is done in this way.

Would you please be so kind and explain in even further detail?

Max
Target Test Prep Representative
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Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)
Re: If 1/2*f(x) = f(x/2), which of the following is true for all values  [#permalink]

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10 Aug 2018, 19:16
2
Bunuel wrote:
If $$\frac{1}{2}f(x) = f(\frac{x}{2})$$, 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 are given that ½f(x) = f(x/2). Let’s analyze the answer choices.

A) f(x) = 2x + 2

½f(x) = ½(2x + 2) = x + 1

f(x/2) = 2(x/2) + 2 = x + 2

We see that A is not true.

B) f(x/2) = 13x

½f(x) = ½(13x) = 13x/2

f(x/2) = 13(x/2) = 13x/2

We see that B is true.

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Re: If 1/2*f(x) = f(x/2), which of the following is true for all values   [#permalink] 10 Aug 2018, 19:16
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