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

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Manager
Joined: 02 Jul 2007
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For which of the following functions f is f(x)=f(1-x) for [#permalink]  05 Sep 2007, 06:18
For which of the following functions f is f(x)=f(1-x) for all 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)
VP
Joined: 10 Jun 2007
Posts: 1464
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Re: GMATPrep; functions [#permalink]  05 Sep 2007, 06:27
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gnr646 wrote:
For which of the following functions f is f(x)=f(1-x) for all 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)

D.

Set x=2, so f(2) = f(-1)
A) f(2) = -1, f(-1) = 2
B) f(2) = -3, f(-1) = 0
C) f(2) = 4-1=3, f(-1) = 1-4=-3
D) f(2) = 4, f(-1) = 4
E) f(2) = -2, f(-1) = -1/2
Manager
Joined: 02 Jul 2007
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[#permalink]  05 Sep 2007, 06:29
got it after looking at how people did the previous post on functions (thanks for that):

f(x)=f(1-x)

plug in "1-x" in for each function and set the two equal to each other.

a) 1-x = 1-(1-x); not true
b) 1-x^2=1-(1-x)^2; not true
c) x^2-(1-x)^2=(x-2)^2-(1-(1-x))^2; not true
d) x^2(1-x)^2=(x-1)^2(1-(1-x))2; true
e) x/(1-x)=(x-1)/(1-(1-x)); not true

answer D.
[#permalink] 05 Sep 2007, 06:29
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# For which of the following functions f is f(x)=f(1-x) for

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