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

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Manager
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Joined: 17 Aug 2006
Posts: 87

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

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New post 12 Nov 2008, 06:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

1) 1-x

2) 1-x^2

3) x^2 - (1-x)^2

4) x^2 (1-x)^2

5) x/(1-x)

I'm not sure how to solve.


The answer is


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

Kudos [?]: 20 [0], given: 0

SVP
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Joined: 30 Apr 2008
Posts: 1863

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Location: Oklahoma City
Schools: Hard Knocks
Re: ARITH 18 OF 37 [#permalink]

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New post 12 Nov 2008, 07:08
Can you please post all answer choices? Then we'll be able to show you a method to solve the question, and other questions like it.

nfa1rhp wrote:
For which of the following functions f is f(x) = f(1-x) for all x?

I'm not sure how to solve.


The answer is


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

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Kudos [?]: 624 [0], given: 32

Manager
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Re: ARITH 18 OF 37 [#permalink]

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New post 13 Nov 2008, 09:09
check

The following are all the answer choices.

1) 1-x

2) 1-x^2

3) x^2 - (1-x)^2

4) x^2 (1-x)^2

5) x/(1-x)

Kudos [?]: 20 [0], given: 0

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Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 322 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12
Re: ARITH 18 OF 37 [#permalink]

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New post 13 Nov 2008, 10:16
nfa1rhp wrote:
For which of the following functions f is f(x) = f(1-x) for all x?

1) 1-x

2) 1-x^2

3) x^2 - (1-x)^2

4) x^2 (1-x)^2

5) x/(1-x)



x^2(1-x)^2=(1-x)^2(1-(1-x)^2, <-- look at this (1-x)^2(1-1+x)^2=(1-x)^2(x)^2

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Manager
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Re: ARITH 18 OF 37 [#permalink]

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New post 13 Nov 2008, 11:45
Its a straight 4 just subsitute x and 1-x in all the answer choices clearly 4 is the answer

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Re: ARITH 18 OF 37 [#permalink]

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New post 13 Nov 2008, 11:51
nfa1rhp wrote:
For which of the following functions f is f(x) = f(1-x) for all x?

1) 1-x

2) 1-x^2

3) x^2 - (1-x)^2

4) x^2 (1-x)^2

5) x/(1-x)

I'm not sure how to solve.


The answer is


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


What you need to do for this type of question is to replace x with 1-x. And other people already showed you how to do that.

Kudos [?]: 11 [0], given: 0

Re: ARITH 18 OF 37   [#permalink] 13 Nov 2008, 11:51
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