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 !

Hi, This problem has been discussed earlier. Please refer to this post https://www.beatthegmat.com/f-x-f-1-x-fu ... 13580.html

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!

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

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

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.