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alltimeacheiver
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Since the correct answer has to work for all values of x, we can plug in a value for x.
Let x=2.
Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1).
The question becomes:
For which of the following functions does f(2) = f(-1)?
Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.
Answer choice B:
f(2) = 1 - 2² = -3.
f(-1) = 1 - (-1)² = 0.
Doesn't work.
Answer choice C:
f(2) = 2² - (1-2)² = 4 - 1 = 3.
f(-1) = (-1)² - [1-(-1)]² = 1-4 = -3.
Doesn't work.
Answer choice D:
f(2) = 2² * (1-2)²= 4 * 1 = 4.
f(-1) = (-1)² * [1-(-1)]² = 1 * 4 = 4.
Success!
Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.
The correct answer is D.
