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M25-22

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M25-22  [#permalink]

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New post 16 Sep 2014, 01:23
2
22
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

37% (01:21) correct 63% (01:22) wrong based on 312 sessions

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Re M25-22  [#permalink]

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New post 16 Sep 2014, 01:23
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9
Official Solution:

If function \(f(x)\) satisfies \(f(x) = f(x^2)\) for all \(x\), which of the following must be true?

A. \(f(4) = f(2)f(2)\)
B. \(f(16) - f(-2) = 0\)
C. \(f(-2) + f(4) = 0\)
D. \(f(3) = 3f(3)\)
E. \(f(0) = 0\)


We are told that some function \(f(x)\) has the following property \(f(x) = f(x^2)\) for all values of \(x\). Note that we don't know the actual function, just this one property of it. For example for this function \(f(3)=f(3^2)\) or \(f(3)=f(9)\), similarly: \(f(9)=f(81)\), so \(f(3)=f(9)=f(81)=...\).

Now, the question asks: which of the following MUST be true?

A. \(f(4)=f(2)*f(2)\): we know that \(f(2)=f(4)\), but it's not necessary \(f(2)=f(2)*f(2)\) to be true (it will be true if \(f(2)=1\) or \(f(2)=0\) but as we don't know the actual function we cannot say for sure);

B. \(f(16) - f(-2) = 0\): again \(f(-2)=f(4) =f(16)=...\) so \(f(16)-f(-2)=f(16)-f(16)=0\) and thus this option is always true;

C. \(f(-2) + f(4) = 0\): \(f(-2)=f(4)\), but it's not necessary \(f(4) + f(4)=2f(4)=0\) to be true (it will be true only if \(f(4)=0\), but again we don't know that for sure);

D. \(f(3)=3*f(3)\): is \(3*f(3)-f(3)=0\)? is \(2*f(3)=0\)? is \(f(3)=0\)? As we don't know the actual function we cannot say for sure;

E. \(f(0)=0\): And again as we don't know the actual function we cannot say for sure.


Answer: B
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Re: M25-22  [#permalink]

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New post 23 Oct 2014, 05:37
1
Bunuel wrote:
Official Solution:

If function \(f(x)\) satisfies \(f(x) = f(x^2)\) for all \(x\), which of the following must be true?

A. \(f(4) = f(2)f(2)\)
B. \(f(16) - f(-2) = 0\)
C. \(f(-2) + f(4) = 0\)
D. \(f(3) = 3f(3)\)
E. \(f(0) = 0\)


We are told that some function \(f(x)\) has the following property \(f(x) = f(x^2)\) for all values of \(x\). Note that we don't know the actual function, just this one property of it. For example for this function \(f(3)=f(3^2)\) or \(f(3)=f(9)\), similarly: \(f(9)=f(81)\), so \(f(3)=f(9)=f(81)=...\).

Now, the question asks: which of the following MUST be true?

A. \(f(4)=f(2)*f(2)\): we know that \(f(2)=f(4)\), but it's not necessary \(f(2)=f(2)*f(2)\) to be true (it will be true if \(f(2)=1\) or \(f(2)=0\) but as we don't know the actual function we cannot say for sure);

B. \(f(16) - f(-2) = 0\): again \(f(-2)=f(4) =f(16)=...\) so \(f(16)-f(-2)=f(16)-f(16)=0\) and thus this option is always true;

C. \(f(-2) + f(4) = 0\): \(f(-2)=f(4)\), but it's not necessary \(f(4) + f(4)=2f(4)=0\) to be true (it will be true only if \(f(4)=0\), but again we don't know that for sure);

D. \(f(3)=3*f(3)\): is \(3*f(3)-f(3)=0\)? is \(2*f(3)=0\)? is \(f(3)=0\)? As we don't know the actual function we cannot say for sure;

E. \(f(0)=0\): And again as we don't know the actual function we cannot say for sure.


Answer: B



Could you please explain as to why E is wrong
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Re: M25-22  [#permalink]

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New post 23 Oct 2014, 10:54
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Rahul2000 wrote:

Could you please explain as to why E is wrong

Hi Rahul2000, in my opinion the reason for it to be wrong is that it doesn't say: f(0) = f(0). It says f(0) = 0 which is not the same. Do you see the difference?
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Re: M25-22  [#permalink]

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New post 07 Dec 2014, 12:34
Request you to please explain the answer with some other method or please explain more elaborately.
Most of these kind of function questions I am unable to understand.
Can you please suggest some study material for the same?
I have already studied MNAHATTAN Books.
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Re: M25-22  [#permalink]

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New post 08 Dec 2014, 05:13
manojpandey80 wrote:
Request you to please explain the answer with some other method or please explain more elaborately.
Most of these kind of function questions I am unable to understand.
Can you please suggest some study material for the same?
I have already studied MNAHATTAN Books.


Check function questions in our Special Questions Directory:

Operations/functions defining algebraic/arithmetic expressions
Symbols Representing Arithmetic Operation
Rounding Functions
Various Functions
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Re M25-22  [#permalink]

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New post 05 Aug 2016, 03:20
I think this is a high-quality question and I agree with explanation.
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Re: M25-22  [#permalink]

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New post 05 Aug 2016, 03:52
Hi,

I resolved this question assuming that a function that satisfies F(x)=F(X^2) for all x is a constant function. Am I correct?
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Re: M25-22  [#permalink]

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New post 11 May 2018, 12:46
So in B, f(-2) can be f(4) or f(16) but f(16) cannot be f(16^2). Why?
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New post 11 May 2018, 13:21
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Re: M25-22  [#permalink]

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New post 28 Jun 2018, 01:34
So, what I understand from this question is that the answer is B because the function described in the question could be stretched to infinity as every number can raised to it's square and there is no given value of x per se. Right, Bunuel ?
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New post 28 Jun 2018, 02:12
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M25-22  [#permalink]

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New post 26 Aug 2019, 11:31
fredurst89 wrote:
Hi,

I resolved this question assuming that a function that satisfies F(x)=F(X^2) for all x is a constant function. Am I correct?

This is was my first thought too (thinking about constant 0,1 output) but it's not necessarily the case that it's a constant. It could be some expression, but it's easier to conceptualize with a constant.

If we test x=0,1 we can see that several answers work, if we test x=10 we can see only B) works:

A) 10 = 10 * 10
B) 10 - 10 = 0
C) 10 + 10 = 0
D) 10 = 3 * 10
E) 10 = 0

The point is to understand that given the square in 2nd function, f(-2) = f(4) = f(16)

Bunuel chetan2u is the above reasoning correct?

Takeaway: when given functions without expressions, just plug (and re-plug) numbers to see what works
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M25-22   [#permalink] 26 Aug 2019, 11:31
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