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For which of the following functions f(x)..

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For which of the following functions f(x)..

by Baby N » Tue Dec 30, 2008 8:04 am
I really don't understand this question, can someone please explain what the question is asking!

For which of the following functions f is f(x) = f(1-x) for all of x?

a) f(x) = 1-x

b) f(x) = 1-x^2

c) f(x) = x^2 - (1-x)^2

d) f(x) = x^2(1-x)^2

e) f(x) = x/1-x

Thanks soo much :) !
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by acecoolan » Tue Dec 30, 2008 8:07 am
Hi,

This problem has been discussed earlier. Please refer to this post

https://www.beatthegmat.com/f-x-f-1-x-fu ... 13580.html
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by Baby N » Tue Dec 30, 2008 1:24 pm
acecoolan wrote:Hi,

This problem has been discussed earlier. Please refer to this post

https://www.beatthegmat.com/f-x-f-1-x-fu ... 13580.html
thanks!
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by vittalgmat » Wed Dec 31, 2008 4:46 am
THis question has been asked so many times and solved so many times as well. Given the frequency, it needs to be added to Resources page.

What do u guys think.??

Moderators: can u pls add the longer version of this discussion to resources?

thanks
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by Rastignac01 » Wed Jan 12, 2011 3:44 pm
Hi Guys,

I think there is an easiest way to solve this kind of questions :

Facinf a question like this, you have to seek for specific value that can "characterize" your fonction f, and that give you clue to define your function .

For instance, with here f(x) = f(1-x), one can easily and quickly notice that f(1)=f(0).

If you notice that, then it very easy to find the solution, replace each function with 0 and 1 instead of x, and see if f(0)=f(1).

WIth A, you have f(1)=0 and f(0)=1, the same for B. For C, f(1)=1 and f(0)=0.
For D f(1)=f(0)=0, that's a match !
the last one is not equal, even not defined for every x, so D is the good answer.

That's a quick method to solve this kind of problem. The more complicated are with more value, therefore you have to make more tests
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by ankur.agrawal » Wed Jan 12, 2011 10:49 pm
Rastignac01 wrote:Hi Guys,

I think there is an easiest way to solve this kind of questions :

Facinf a question like this, you have to seek for specific value that can "characterize" your fonction f, and that give you clue to define your function .

For instance, with here f(x) = f(1-x), one can easily and quickly notice that f(1)=f(0).

If you notice that, then it very easy to find the solution, replace each function with 0 and 1 instead of x, and see if f(0)=f(1).

WIth A, you have f(1)=0 and f(0)=1, the same for B. For C, f(1)=1 and f(0)=0.
For D f(1)=f(0)=0, that's a match !
the last one is not equal, even not defined for every x, so D is the good answer.

That's a quick method to solve this kind of problem. The more complicated are with more value, therefore you have to make more tests
Hi i found this solution most efficient. Can u confirm whether this logic will always hold true for these type of questions.
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