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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 17 Oct 2007, 18:20
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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/(x-1)
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2593
Followers: 16

Kudos [?]: 198 [0], given: 0

 [#permalink] New post 17 Oct 2007, 18:21
Let me know if im finally getting how to do these crazy functions.
(sorry long post and I may have errors... Please note if my algebra is messed up!!!)

1) f(x)= 1-x

f(1-x)=1-(1-x) --> x not equalt to f(x)

2) f(x)= 1-x^2
f(1-x)=1-(1-x)^2 --> 1-(1-2x+x^2) ---> 1-1+2x-x^2 --> 2x-x^2 not equal to f(x)

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

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

1-2x+x2-x^2 --> 1-2x. not equal to f(x)

not equal to f(x)

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

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

Thus 4 is the answer

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

f(1-x) = 1-x/1-(1-x) ---> 1-x/1-1+x --> 1-x/x

not equal to f(x)

OA is D.
  [#permalink] 17 Oct 2007, 18:21
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For which of the following functions f is f(x)= f(1-x) for

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