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

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SVP
Joined: 16 Oct 2003
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For which of the following functions f is f(x) = f(1 - x) [#permalink]  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
Manager
Joined: 02 Oct 2005
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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.
CEO
Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Scanning the answers choices gives you D in just 10 -15 seconds. Hoping to see these questions in real GMAT.
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
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yeah D it is ! had to work out.. cldnt get in a scan !
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VP
Joined: 20 Sep 2005
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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.
Senior Manager
Joined: 13 Jun 2005
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Location: Haverhill, MA
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I got D too..
But did work it out..
Have to start thinking smart...
Intern
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Re: From GMATPrep Function f(x) [#permalink]  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
Director
Joined: 04 Oct 2005
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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
VP
Joined: 21 Sep 2003
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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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Manager
Joined: 23 Jan 2006
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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?
Manager
Joined: 19 Jul 2005
Posts: 67
Location: Atlanta
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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.
Manager
Joined: 23 Jan 2006
Posts: 192
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Kudos [?]: 12 [0], given: 0

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
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