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If function f(x) satisfies f (1-x) = f (2+x) for all

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Senior Manager
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Joined: 31 Jul 2017
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Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
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WE: Consulting (Energy and Utilities)
If function f(x) satisfies f (1-x) = f (2+x) for all  [#permalink]

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New post 16 Sep 2018, 23:44
3
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

33% (02:05) correct 67% (02:14) wrong based on 9 sessions

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If function f(x) satisfies f (1-x) = f (2+x) for all x, which of the following can be true?

1. f(x) = \(3-x\)
2. f(x) = \(1-x^2\)
3. f(x) = \(2 - x - x^2\)
4. f(x) = \(2x - (1-x)^2\)
5. f(x) = \((1-x) / (2 + x)\)

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Re: If function f(x) satisfies f (1-x) = f (2+x) for all  [#permalink]

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New post 18 Sep 2018, 19:32
The answer is C. The question is asking for a function symmetric about x=-0.5. A, D & E are not even functions, so they can't be symmetric. B is symmetric about 0. And C simplifies to

2.25-(x+0.5)^2.

Thus it is symmetric about x= -0.5.
GMAT Club Bot
Re: If function f(x) satisfies f (1-x) = f (2+x) for all &nbs [#permalink] 18 Sep 2018, 19:32
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