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

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For which of the following functions f is f(x) = f(1 - x) [#permalink] New post 22 Jan 2006, 22:57
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 22 Jan 2006, 23:02
Though the easier way if to simply scan through the ans choices and D comes across as an easy answer, i am posting the detailed soln as well.

A) f(1-x) = 1-(1-x) = x
B) f(1-x) = 1-(1-x)^2 not equal to 1-x^2 for all values of x
C) f(1-x) = (1-x)^2 - x^2 = 1-2x not equal to f(x)
D) Correct
E) f(1-x) = (1-x)/x not equal to f(x) for all x

D clearly.
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 [#permalink] New post 23 Jan 2006, 01:37
Scanning the answers choices gives you D in just 10 -15 seconds. Hoping to see these questions in real GMAT. :-D
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 [#permalink] New post 23 Jan 2006, 11:24
yeah D it is ! had to work out.. cldnt get in a scan !
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 [#permalink] New post 23 Jan 2006, 12:47
Got D...in around 90 seconds. Didn't scan..worked it out in reverse order. Trust ETS to make me work through all the answer choice and keep the answer at D or E.
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 [#permalink] New post 23 Jan 2006, 15:01
I got D too..
But did work it out..
Have to start thinking smart...
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Re: From GMATPrep Function f(x) [#permalink] New post 23 Jan 2006, 18:11
[quote="Bhai"]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[/quote]

got D. but had to calculate
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 [#permalink] New post 23 Jan 2006, 22:30
i guess one should always scan from the last choice..i looked at the first and then solved it, then second and so spent 1.5 min
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 [#permalink] New post 23 Jan 2006, 23:50
Yep only D is the correct answer.

Infact functions of this type are called symmetric functions. A function that is unchanged by any permutation of its variables.

Egs:
f(x,y) = x*y
f(x,y) = x+y
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 [#permalink] New post 24 Jan 2006, 07:08
I had to work it out.
Can somone explain how they were able to "scan" it? Is there a certain property you recognized, or is it just pure intuition?
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 [#permalink] New post 24 Jan 2006, 07:17
I have no idea what this question is asking for. Can some one explain this question? Oh, and sorry for the broad question, I don't even know what to ask.

Thanks.
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 [#permalink] New post 24 Jan 2006, 07:50
giddi77 wrote:
Yep only D is the correct answer.

Infact functions of this type are called symmetric functions. A function that is unchanged by any permutation of its variables.

Egs:
f(x,y) = x*y
f(x,y) = x+y


giddi77,
How are those symmetric funcitons?
f(x,y) = x*y
ley x=10, y=5
f(x,y) = 10*5 =50
f(x+2, y-1) = 12*4 = 48
  [#permalink] 24 Jan 2006, 07:50
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