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

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

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01 Sep 2005, 06:14
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For which of the following functions 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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01 Sep 2005, 08:09
D, gives the same result when x, is subst with 1-x
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02 Sep 2005, 00:09
Can you show your work? I don't understand even how to approach this...thanks!
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02 Sep 2005, 04:18
D again.

Replace 1-x in the given functions and check which one equals F(x).

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06 Sep 2005, 13:26
Can someone please explain how to approach this problem?

thx
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07 Sep 2005, 03:59
For which of the following functions 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)

so subsitute 2
f(x) = f(1-x)
f(2) = f(1-2)
x^2(1-2)^2 = (1-2)^2(1-(1-2)^2
(4)((-1)^2) = ((-1)^2)(2^2)
4 = (1)(4)
4 = 4

Try it with 3
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07 Sep 2005, 23:36
edsilver wrote:
Can someone please explain how to approach this problem?

thx

For which of the following functions 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)

Place x=1-x in the above expressions and see the results. Start from c

f(1-x)= (1-x)^2-(1-1+x)^2= (1-x)^2-x^2 which is not equal ro the F(X) expression.

Try D
(1-x)^2 (1-1+X)^2 = (1-x)^2 x^2 OR x^2(1-x)^2 Same as f(x) SO D is the answer
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