GMAT function problem

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m_aspirant: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Sep 23, 2011 6:13 pm

by m_aspirant » Wed Sep 28, 2011 10:00 am

I can't seem to understand how to solve following function problem (from GMAT CAT - practice test):-
^ : square
____________

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

A. f(x) = f(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)

The correct answer is D. But I don't know how to solve it.

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Source: Beat The GMAT — Problem Solving | Wed Sep 28, 2011 10:00 am

user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Wed Sep 28, 2011 4:49 pm

are you sure option A is correct?
because that is what is given in question to check for.

and also nothing seems to follow f(x) = f(1-x) especially D
it could have been correct, if it is f(x) = x^2(1-x)^2

regards,
user123321

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Sep 28, 2011 5:44 pm

i made a mistake below, by counting (a+c)^2 as a+c^2
by taking the right-hand-side of function and supplying (x-1) instead of x. We should solve for difference between two sides to obtain 0

solution:
A. f(x) = f(1-x)==> 1-x=1-(x-1), -1 is not equal to 0
B. f(x) = 1-x^2 ==> 1-x^2=1-(x-1)^2, 1-x^2-1+(x^2-2x+1), 1-2x is not equal to 0 for all x
C. f(x) = x^2-(1-x^2)==> 2x^2-1=2(x-1)^2-1, 2x^2-1-2(x^2-2x+1)+1, 4x-2 is not equal to 0 for all x
D. f(x) = x^2(1-x^2) ==> x^2(1-x^2)=(x-1)^2 * (1-(x-1)^2
E. f(x) = x/(1-x) ==> x/(1-x)= (x-1)/(1-(x-1)
x/(x-1)= (x-1)/(2-x), x(2-x)=(x-1)^2, 2x-x^2=x^2-2x+1, 2x^2-4x+1 is not equal to 0 for all x

d

m_aspirant wrote:I can't seem to understand how to solve following function problem (from GMAT CAT - practice test):-
^ : square
____________

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

A. f(x) = f(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)

The correct answer is D. But I don't know how to solve it.

Last edited by pemdas on Thu Sep 29, 2011 1:30 am, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Sep 28, 2011 6:13 pm

m_aspirant wrote:I can't seem to understand how to solve following function problem (from GMAT CAT - practice test):-
^ : square
____________

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

A. f(x) = f(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)

The correct answer is D. But I don't know how to solve it.

Let us look at each of the options:

(A) f(x) = 1-x
f(1-x) = 1 - (1-x) = x; FALSE

(B) f(x) = 1-x^2
f(1-x) = 1 - (1-x)^2 = 1 - (1 - 2x + x^2) = 2x - x^2; FALSE

(C) f(x) = x^2 - (1-x)^2
f(1-x) = (1-x)^2 - (1 - (1-x))^2 = 1 - 2x + x^2 - (x)^2 = 1 - 2x; FALSE

(D) f(x) = x^2 * (1-x)^2
f(1-x) = (1 - x)^2 * (1 - (1 - x))^2 = (1 - x)^2 * (x)^2; TRUE

(E) f(x) = x/(1-x)
so f(1-x) = (1-x)/(1-(1-x)) = (1-x)/x; FALSE

The correct answer is D.

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studentps2011: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Fri Jul 15, 2011 5:37 am; Thanked: 3 times

by studentps2011 » Thu Sep 29, 2011 10:10 am

It can also be solved by plugging in a number for x (for eg: x=0 and so, 1-x=1)

In other words, we need to check for equations where f(0) = f(1)

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 29, 2011 1:32 pm

I posted a solution here:

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