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f(x)=f(1-x) for all x?

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jackiesong83
 Post subject: f(x)=f(1-x) for all x?
 Post Posted: Sun Jan 24, 2010 10:35 pm 
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Course Students


Posts: 6
For which of the folloiwng 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

help.
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sarathsasikumar
 Post subject: Re: f(x)=f(1-x) for all x?
 Post Posted: Mon Jan 25, 2010 5:58 pm 
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Students


Posts: 16
Answer is D f(x) = x^2(1-x)^2

Try replacing "x" with "1-x" in each of the options. In a, b,c and d you will find that f(x) is not equal to f(1-x).

But in D,

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

So, f(1-x) equals (1-x)^2 [1- (1-x)]^2 = (1-x)^2 x^2 which is the same as f(x).

Hence D
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RonPurewal
 Post subject: Re: f(x)=f(1-x) for all x?
 Post Posted: Tue Feb 09, 2010 7:09 am 
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ManhattanGMAT Staff


Posts: 7146
there are already many, many posts on this problem. please search the forums before posting it yet again!

here's one:
for-which-of-the-following-functions-f-is-f-x-f-1-x-for-t283.html
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