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problem solving

by MichelleW1982 » Mon Apr 20, 2009 5:28 pm
For which of the following functions f is f(x)=f(1-x) for all x?

Sorry I dont have all the answer choices, but the correct answer is

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

can anyone walk me through this?
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by dmateer25 » Mon Apr 20, 2009 5:57 pm
Just fill in 1-x for x and see which answer choice it works for.

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


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

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

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

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


or use numbers

f(2) = 2^2 (1-2)^2
f(2) = 4 * (-1)^2
f(2) = 4 *1
f(2) = 4


f(1-2) = (1-2)^2 * ( 1 - 1 - 2)^2
f(1-2) = (-1)^2 * (-2)^2
f(1-2) = 1 * 4
f(1-2) = 4
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