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

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Director
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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
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (02:44) correct 71% (03:01) wrong based on 32 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.
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Re: If function f(x) satisfies f (1-x) = f (2+x) for all   [#permalink] 18 Sep 2018, 19:32
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