## f(x) = f(1-x) function problem q

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#### f(x) = f(1-x) function problem q

* Sun Jul 06, 2008 2:13 pm*
Elapsed Time: **00:00**
- Lap #[LAPCOUNT] ([LAPTIME])

f(x) = f(1-x)

A f(x) = 1-x

B f(x) = 1-x^2

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

D d. f(x) = x^2(1-x)^2 EDITED

E f(x) = x / 1-x

The correct answer is D. However, can someone elaborate on how to approach the problem? If I substitute 2 in D I get f(2) = 4 (1-2)^2 =>

2 = 4. What am I missing?

Last edited by czechchamp on Mon Jul 07, 2008 6:40 am; edited 1 time in total

* Sun Jul 06, 2008 7:10 pm*
f(x) = f(1-x)

let us consider the choices:

option D

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

substitute 1-x in the place of x in equation 1we have

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

==>(1-x)^2*(x)^2==>x^2*(1-x)^2----(2)

1=2

so Option D only satisfies

(OR)

The correct answer is D. However, can someone elaborate on how to approach the problem? If I substitute 2 in D I get f(2) = 4 (1-2)^2 =>

2 = 4. What am I missing?

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

substitute 2 in equation (a)

==>4(1-2)^2==>4

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

so substitute f(-1 ) in equation (a)

==(-1)^2(1-(-1))^2==>2^2==>4

so D is the answer

* Sun Jul 06, 2008 10:03 pm*
is it a typo...option D doesnt seem to be right

it says (1-x)

Whereas in the solution it sez (1-x)^2

Please correct me if im wrong

im just a newbie...

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* Mon Jul 07, 2008 4:57 am*
czechchamp wrote

If I substitute 2 in D I get f(2) = 4 (1-2)^2 =>

2 = 4. What am I missing?

so,option D should be

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

i think he forgot to write ^2 in option D

* Mon Jul 07, 2008 6:39 am*
**sibbineni wrote:**czechchamp wrote

If I substitute 2 in D I get f(2) = 4 (1-2)^2 =>

2 = 4. What am I missing?

so,option D should be

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

i think he forgot to write ^2 in option D

Yes, indeed, I keyed it in wrong. The option D as noted above should be f(x) = x^2(1-x)^2

Thanks for your explanation!

* Mon Jul 07, 2008 7:21 am*
on this type of question - is the best/q

uickest way to solve this equation to plug in the functions into each of the answer choices? Is there a special GMAT shortcut or is this question painfully slow?

* Wed Oct 08, 2008 2:56 am*
As I have learnt,depends form problem to problem.

Here just substitute (1-x) for all functions.

We get f(x)=f(1-x)=f(x) right away.

* Sat May 16, 2009 3:41 am*
is there a more simple way to word this question? What is being asked is very convoluted.

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* Fri May 29, 2009 12:32 pm*
[quote="aj5105"]As I have learnt,depends form problem to problem.

Here just substitute (1-x) for all functions.

We get f(x)=f(1-x)=f(x) right away.

EDIT: actually that seems to be the fastest way

* Sat Jun 27, 2009 1:29 pm*
I am having a lot of trouble understanding these type of a problems. Can someone please explain this in the most rudimentary way, from the basics of what is f(x) to what the question is seeking.

It will be greatly appreciated.

Thanks,

Vineet

* Fri Aug 28, 2009 10:41 am*
Hi, I had hard times also.

The question gives you 5 different functions and asks for which of the functions plugging in the value of x gives the same result of plugging (1-x).

basically, just substitute (1-x)at x and see if they give you the same result:

for example if you look at the first function:

F(x)=1-x

F(1-x) = 1-(1-x)=-x

They give you different results so this functions is not that function that gives you the same result using x or (1-x).

Let's have a look to the right one (D).

F(X)= (x^2) * (1-x)^2

F(1-X)= (1-x)^2 * ((1-(1-x))^2 = (1-x)^2 * (-x)^2 = (1-x)^2 * x^2

So you get that same equation using x or (1-x).

Goof luck for your studies.

Mat

* Mon Nov 16, 2009 1:25 pm*
I'm not sure I understand this.

So we plug in x-1 for x for all the equations. Then what are we looking out for that gives D as the answer?

Thanks!

* Mon Mar 22, 2010 6:07 pm*
I'm sure that this question has been discussed many a times. But everywhere, plugging in seems the only option to solve.

How do you solve this without plugging in?

* Mon May 24, 2010 4:37 pm*
The question is asking for (at which of the following f(x)=f(1-x)).

and that could only be true by using the formula of choice D

but what is worth to be asked: How do I solve this problem in less than 2 minutes!!!

I think if you face this kind of question, try to make a guess, this kind of question is to make the probability of one scoring

800 is very low!

* Sat Jun 19, 2010 4:59 am*
We would appreciate it if an EXPERT may inspire us on how to tackle those types of problems (functions) on the gmat,and how to solve this one specifically.

THANKS!