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

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For which of the following functions f is f(x) = f(1- x) for [#permalink] New post 29 Sep 2006, 18:24
For which of the following functions f is f(x) = f(1- x) for all x?

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



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 [#permalink] New post 30 Sep 2006, 05:56
For these type of questions you have to go through all the solutions. Starting from the bottom is advisable most of the time.


f(x) = 1 -x , f(1 - x) = 1 - ( 1 - x) = x

f(x) = 1 -x^2 , f(1 - x) = 1 - (1 - x)^2 = 1 - (1 - 2x + x^2)

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

f(x) = x^2 (1 -x)^2 , f(1 - x) = ( 1 - x)^2 (1 - (1 - x))^2 = ( 1 - x)^2 x ^ 2 (BINGO)
f(x) = x / 1-x , f(1 - x) = ( 1- x ) / ( 1 - (1- x)) = (1 - x)/x


Hence D
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 [#permalink] New post 30 Sep 2006, 06:23
Hate to sound like a moron but what's is the relevance of the following :

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

Is that equal to f(x) = f(1-x)

??
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 [#permalink] New post 30 Sep 2006, 06:26
No problem everyone is here to learn.

The idea of this whole problem is to replace x with 1 - x , and find the function that gives the SAME result for both of them.

Cheers
  [#permalink] 30 Sep 2006, 06:26
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