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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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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?

Thanks in advance,
Max
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Re: If 1/2*f(x) = f(x/2), which of the following is true for all values [#permalink]
maxmayr wrote:
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?

Thanks in advance,
Max



I was wondering the same. Would someone kindly explain this? Thank you in advance.
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If 1/2*f(x) = f(x/2), which of the following is true for all values [#permalink]
Expert Reply
owlette wrote:
maxmayr wrote:
chetan2u wrote:

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?

Thanks in advance,
Max



I was wondering the same. Would someone kindly explain this? Thank you in advance.



Ok..
When f(x) = 2x+2, what will be f(2). It will be 2(2)+2=6.
So. it is only the x which gets effected...

Say \(f(\frac{x}{2}) = 2x+2\), and we are looking for f(x).
Here we will get the term of x in terms of x/2, so \(f(\frac{x}{2})=2x+2=2*x*\frac{2}{2}+2=2*2(\frac{x}{2})+2=4(\frac{x}{2})+2\)..
so f(x) will be 4x+2
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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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