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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: 51185
If 1/2*f(x) = f(x/2), which of the following is true for all values  [#permalink]

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30 Jul 2018, 23:14
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Difficulty:

45% (medium)

Question Stats:

57% (01:15) correct 43% (01:22) wrong based on 69 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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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, 00:45
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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, 01:28
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
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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, 18:16
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 &nbs [#permalink] 10 Aug 2018, 18:16
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