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

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For which of the following functions does f(x)=f(2-x)? [#permalink]

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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
[Reveal] Spoiler: OA
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Re: For which of the following functions does f(x)=f(2-x)? [#permalink]

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New post 11 Jul 2013, 09:17
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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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Re: For which of the following functions does f(x)=f(2-x)? [#permalink]

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New post 11 Jul 2013, 09:20
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Expert's post
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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Re: For which of the following functions does f(x)=f(2-x)? [#permalink]

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New post 11 Jul 2013, 09:54
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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New post 22 Dec 2014, 09:50
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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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Re: For which of the following functions does f(x)=f(2-x)? [#permalink]

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New post 23 Feb 2017, 18:34
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.
Re: For which of the following functions does f(x)=f(2-x)?   [#permalink] 23 Feb 2017, 18:34
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