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Manager  Joined: 01 Jul 2012
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Location: United States
GMAT 1: 510 Q34 V28 GMAT 2: 580 Q35 V35 GMAT 3: 640 Q34 V44 GMAT 4: 690 Q43 V42 GPA: 3.61
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For which of the following functions does f(x)=f(2-x)?  [#permalink]

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10 00:00

Difficulty:   45% (medium)

Question Stats: 65% (01:36) correct 35% (01:53) wrong based on 502 sessions

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For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4?
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1
Director  Joined: 14 Dec 2012
Posts: 745
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34 GPA: 3.6
Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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josemnz83 wrote:
For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4?
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1

hi,

in all the option just put 2-x in place of x

A. f(x)=x+2===>f(2-x)=2-x+2=4-x==>not equal

B. (fx)=2x-x^2====>f(2-x)=2(2-x)-(2-x)^2=4-2x-x^2+4x-4=2x-x^2===>equal==correct

C. f(x)=2-x===>f(2-x)=2-(2-x)=x===>not equal

D. f(x)=(2-x)^2===>f(2-x)=(2-2+x)^2=x^2===>not equal

E. f(x)=x^2===>f(2-x)=(2-x)^2===>not equal

hence only B satisfies.

dont plug in this

hope it helps.
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Math Expert V
Joined: 02 Sep 2009
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Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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josemnz83 wrote:
For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4?
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1

If you plug x=1 then all options will work, since f(x)=f(1) and f(2-x)=f(1) too. For such kind of questions it's not a good idea to plug 0, -1 or 1.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

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Hope it helps.
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Manager  Joined: 24 May 2013
Posts: 79
Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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josemnz83 wrote:
For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4?
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1

If we plug x=0 then, f(0)=f(2)
A. F(0)= 2 and f(2)= 4
B. f(0)= 0 and f(2)= 0
C. F(0)= 2 and f(2)= 0
D. F(0)= 4 and f(2)= 0
E. f(0)= 0 and f(2)= 4

Hence b is the correct answer.
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Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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1
It can be easily done in less than a minute simply by elimination or substitution method.

1) f(x)=x+2; for x=2-x , f(2-x)=4. Eliminated
2) f(x) = 2x-x^2; for x=2-x ,f(2-x)=2(2-x)-(2-x)^2 =(2-x)(2-2+x)=2x-x^2
3) f(x) = 2 - x; for x=2-x, f(2-x)=x . Eliminated
4) f(x)=(2-x)^2; for x=2-x, f(2-x)=(x)^2 . Eliminated
5) f(x)=x^2;for x=2-x, f(2-x)=(2-x)^2. Eliminated
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Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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What confuses my about this question, with answer "B," is an example in which you have f(2-3)

f(2-3)=-1

F(x)= 2(2-x)-(2-x)^2
F(2-3)= 2(2-3)-(2-3)^2
F(2-3)= 2(-1)-(-1)^2
F(2-3)= -2-1
F(2-3)= -3?

Maybe I'm tired or something but I keep coming to this conclusion.
Manager  B
Joined: 31 Dec 2016
Posts: 73
For which of the following functions does f(x)=f(2-x)?  [#permalink]

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Nunuboy1994 wrote:
What confuses my about this question, with answer "B," is an example in which you have f(2-3)

f(2-3)=-1

F(x)= 2(2-x)-(2-x)^2
F(2-3)= 2(2-3)-(2-3)^2
F(2-3)= 2(-1)-(-1)^2
F(2-3)= -2-1
F(2-3)= -3?

Maybe I'm tired or something but I keep coming to this conclusion.

A good way to solve it is like this. Essentially the question is saying F(X) so everytime you see an X you're going to sub in the function 2-x. A good video explaining how functions work is here since most people here do a crappy job. https://www.youtube.com/watch?v=T6-Zdr5w_bE
Attachments Function question 3.png [ 292.42 KiB | Viewed 27207 times ]

Senior Manager  G
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Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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josemnz83 wrote:
For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

Answer choice C seems to work out if we plug in 1 for x. Did I do something wrong or must the function be true for all values? C does not work for a value of x=4?
f(x)=2-1=1
f(x)= 2-(2-x).....>2-(2-1).....>2-(1) = 1

hi

let f(0) = f(2)

B: f(0) = 0
f(2) = 4 - 4 = 0

so f(0)= f(2)
B is the answer

thanks
VP  G
Joined: 09 Mar 2018
Posts: 1007
Location: India
Re: For which of the following functions does f(x)=f(2-x)?  [#permalink]

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josemnz83 wrote:
For which of the following functions does f(x)=f(2-x)?

A. f(x)=x+2
B. (fx)=2x-x^2
C. f(x)=2-x
D. f(x)=(2-x)^2
E. f(x)=x^2

A. f(x)=x+2
f(2-x) = 2-x+2, Not equal

B. f(x)=2x-x^2
f(2-x) = 2*(2-x) - (2-x)^2 = 4-2x- [ 4 + x^2 - 4x] = 2x-x^2

C. f(x)=2-x
f(2-x) = 2-2+x = x, Not equal

D. f(x)=(2-x)^2
f(2-x)= (2-2-x)^2 , Not equal

E. f(x)=x^2
f(2-x) = (2-x)^2, Not equal

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Many of life's failures happen with people who do not realize how close they were to success when they gave up. Re: For which of the following functions does f(x)=f(2-x)?   [#permalink] 11 Jan 2019, 22:03
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