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

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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 09 Feb 2007, 21:06
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?

a) f(x) = 1-x
b) f(x) = 1-x^2
c) f(x) = x^2 - (1-x)^2
d) f(x) = x^2(1-x)^2
e) f(x) = x/1-x
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Re: Functions problem [#permalink]

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New post 09 Feb 2007, 21:14
above720 wrote:
For which of the following functions f is f(x) = f(1-x) for all x?

a) f(x) = 1-x
b) f(x) = 1-x^2
c) f(x) = x^2 - (1-x)^2
d) f(x) = x^2(1-x)^2
e) f(x) = x/1-x


f(x) = f(1-x): If we substitute (1-x) in the choice a, b, c, .. below. One of them will not change form.

a) f(1-x) = 1 - (1-x) = 1 - 1 + x = x. Function is changed. False
..
d) f(1-x) = ((1-x)^2)*(1- 1 + x)^2 = (1-x)^2 * x^2. Function remains the same. True

D. is the answer
Re: Functions problem   [#permalink] 09 Feb 2007, 21:14
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For which of the following functions f is f(x) = f(1-x) for

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