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Function f(x) satisfies f(x) =

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Function f(x) satisfies f(x) = [#permalink]

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New post 03 Oct 2008, 23:11
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Function \(f(x)\) satisfies \(f(x) = f(x^2)\) for all \(x\) . Which of the following must be true?

* \(f(4) = f(2)f(2)\)
* \(f(16) - f(-2) = 0\)
* \(f(-2) + f(4) = 0\)
* \(f(3) = 3f(3)\)
* \(f(0) = 0\)

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Re: Symbols [#permalink]

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New post 04 Oct 2008, 05:38
* F(16)-f(-2)=0
On the above leads to f(16)-f(16).

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New post 04 Oct 2008, 05:54
Agree with (B)

f(x) = f(x^2)

f(-2) = f(4) = f(16)

:)

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New post 04 Oct 2008, 06:51
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Can someone explain what each answer choice leads to?

And the logic behind solving the question...

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New post 07 Oct 2008, 05:27
i think this is a cryptic one - can someone pls. each individual answer choice analyse (i know it´s bit of work, but it would really help those who are not 100% understaning the concept of functions).

many thanks in advance
dom

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New post 07 Oct 2008, 13:58
domleon wrote:
i think this is a cryptic one - can someone pls. each individual answer choice analyse (i know it´s bit of work, but it would really help those who are not 100% understaning the concept of functions).

many thanks in advance
dom


Don't be fooled by big words like functions ect. there is nothing really to know.

In every function f(x) = 2x when you enter some value (lets assume x=2) you get a value (in this case 4) so if you just ignore the notation f(x) you can just write:

2x = ? for x=2

but a nice thing about functions is that you can take the outcome and reinstall it in the original function to get another (third) value.

f(x)=2x

f(x)=2(2x) = 4x

and so on ...

In this question you are not asked about values at all, you are being asked about functions and functions of functions so:

f(x) = f(x^2)

f(2) = f(2^2)

f(3) = f(3^3)

and so on...

we can't tell the value of f(2) = ?? only that it's equal to some f(4)

back to the question asked:

f(x) = f(x^2) is given

first line:

f(-2) = f(4) according to the given f(x) = f(x^2)

f(4) = f(16) according to the given f(x) = f(x^2)

f(4) = f(2)*f(2) ??

we have seen that f(4) = f(16) & f(2) = f(4) but we cannot say that f(4) = f(2)*f(2)

this may be true but we cannot say that from the given f(x) = f(x^2)

second line:

f(16)-f(-2) = 0

we can say that f(16) = f(-2) from the given data since:

f(-2) = f(4)

f(4) = f(16)

so we can say this is true !

third line:

f(-2)+f(4) = 0

we can't say if this is true since we don't know what is the value of f(-2) but we can tell that f(-2) = f(4) useless here !

forth line:

f(3) = 3f(3)

since f(3) = f(9)

I dont see how we can say this is true without knowing what f(3) = ??

fifth line:

f(0) = 0

we only know that f(0) = f(0) but we know nothing about 0


hopes this will help

:)

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Re: Symbols [#permalink]

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New post 09 Oct 2008, 01:22
greenberg -many thanks for the good explaination!

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Re: Symbols   [#permalink] 09 Oct 2008, 01:22
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