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

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

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...

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

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!

on this type of question - is the best/quickest 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?

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.

is there a more simple way to word this question? What is being asked is very convoluted.

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

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

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!

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?

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!

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!