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

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

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28 Jun 2011, 07:12
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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)

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html
[Reveal] Spoiler: OA

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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 08:09
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Baten80 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)

For

x=1;
1-x=0

a) f(1)=1-1=0; f(0)=1-0=1
b) f(1)=1-1=0; f(0)=1-0=1
c) f(1)=1-(1-1)^2=1-0=1; f(0)=0-(1-0)^2=-1
d) f(1)=1*(1-1)^2=0; f(0)=0---- Correct. f(1)=f(0)
e) f(1)=1/0=undefined; f(0)=0

Ans: "D"
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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07 Aug 2011, 04:30
1
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DeeptiM wrote:
fluke wrote:
Baten80 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)

For

x=1;
1-x=0

a) f(1)=1-1=0; f(0)=1-0=1
b) f(1)=1-1=0; f(0)=1-0=1
c) f(1)=1-(1-1)^2=1-0=1; f(0)=0-(1-0)^2=-1
d) f(1)=1*(1-1)^2=0; f(0)=0---- Correct. f(1)=f(0)
e) f(1)=1/0=undefined; f(0)=0

Ans: "D"

Thanks for directing me here fluke..need your help with point c and d..

we took x=1 and 1-x=0..if so then c should be
f(x) = x^2 - (1-x)^2 -------- Original Statement
1 = 1 - (0)^2 {:Note: Here LHS should be f(1) not 1. You need to consider both case one by one}
1=1

and d should be
f(x) = x^2 * (1-x)^2 -------- Original Statement
1 = 1 * (0)^2
1=0

I am sure there is a miss in my understanding for which i need your help.

If there is a function;
f(x)=x-1
f(1)=1-1=0
f(2)=2-1=0
f(z)=z-1
f(1+x)=1+x-1=x

You see how we replace x with whatever is in the bracket of f().

Likewise;
f(x) = x^2 - (1-x)^2
f(1)=(1)^2-(1-1)^2=1-0=1 {:Note: Replace x with 1}
f(0)=0^2-(1-0)^2=0-1=-1 {:Note: Replace x with 0}

You see:
f(1) NOT EQUAL f(0). Thus, it is incorrect.

We can't do partial replacement.

Or algebraically:

C:
f(x) = x^2 - (1-x)^2= x^2-(1+x^2-2x)=x^2-1-x^2+2x=2x-1
f(1-x)=(1-x)^2 - (1-(1-x))^2=1+x^2-2x-x^2=1-2x {:Note: I replaced x with 1-x everywhere}

Try the same with D yourself.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:17
It's D, a quick inspection reveals the symmetry of the expressions.

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

Substitute x with (1-x) :

f(1-x) = (1-x)^2 (1-1+x)^2 = (1-x)^2 * x^2 = f(x)
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:23
subhashghosh wrote:
It's D, a quick inspection reveals the symmetry of the expressions.

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

Substitute x with (1-x) :

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

please make me understand the "quick inspection process."
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:27
I meant a quick scan of choices in general
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:29
Baten80 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)

u need to try each option..
a. 1-x = 1-(1-x)= X ............ No
b 1-x^2 = same as above ........ No
3. X^2-(1-X)^2 = (1-x)^2- (1-1+X)^2
= (1-x)^2- X^2............. No
4. x^2*(1-x)^2= (1-x)^2(1-(1-X))^2
= (1-x)^2*x^2............... yes
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:36
sudhir18n wrote:
Baten80 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)

u need to try each option..
a. 1-x = 1-(1-x)= X ............ No
b 1-x^2 = same as above ........ No
3. X^2-(1-X)^2 = (1-x)^2- (1-1+X)^2
= (1-x)^2- X^2............. No
4. x^2*(1-x)^2= (1-x)^2(1-(1-X))^2
= (1-x)^2*x^2............... yes

Basically I did it at the test.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 07:40
We don't need to try every option, e.g., A and E are not possible is clear at the first glance.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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28 Jun 2011, 08:43
I also got this same question on my yesterday gmat prep practice test1 and I tried the same way as Fluke did and ended up with answer shoice D.

sometime we have to put some number in the answer choice and see if that matches with the question asked ...

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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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29 Jun 2011, 16:19
substituting x with 1-x and verifying the f(x) and f(1-x) in the answer choices, we can see that Answer is D.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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29 Jun 2011, 16:37
I arrived at D but over the 2 minute benchmark. Seems like I need to work on finding ways to eliminate choices off the bat as I tested each option for this question.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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07 Aug 2011, 04:02
fluke wrote:
Baten80 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)

For

x=1;
1-x=0

a) f(1)=1-1=0; f(0)=1-0=1
b) f(1)=1-1=0; f(0)=1-0=1
c) f(1)=1-(1-1)^2=1-0=1; f(0)=0-(1-0)^2=-1
d) f(1)=1*(1-1)^2=0; f(0)=0---- Correct. f(1)=f(0)
e) f(1)=1/0=undefined; f(0)=0

Ans: "D"

Thanks for directing me here fluke..need your help with point c and d..

we took x=1 and 1-x=0..if so then c should be
f(x) = x^2 - (1-x)^2 -------- Original Statement
1 = 1 - (0)^2
1=1

and d should be
f(x) = x^2 * (1-x)^2 -------- Original Statement
1 = 1 * (0)^2
1=0

I am sure there is a miss in my understanding for which i need your help.
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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07 Aug 2011, 05:06
Awsum..i get it now..

Thanks Fluke..for the great explanation and above all your patience!!
Kudos to you!
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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27 Feb 2013, 02:06
As a General Strategy is it good to test 0 and 1 for these questions?
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Re: For which of the following functions f is f(x) = f(1-x) for [#permalink]

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27 Feb 2013, 02:25
fozzzy wrote:
As a General Strategy is it good to test 0 and 1 for these questions?

Check this post: for-which-of-the-following-functions-f-is-f-x-f-1-x-for-85751.html#p644387 (plug in numbers method)
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Re: For which of the following functions f is f(x) = f(1-x) for   [#permalink] 27 Feb 2013, 02:25
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