I'll get you going on this one... you should see if you can work out the rest of it on your own.
The question is asking us to identify which function from among the five given has the property that f(x) = f(1 - x). That is, "plugging in" x into f yields the same result as plugging in 1 - x into f.
Let's show option A does NOT have this property:
f(x) = 1 - x
f(1 - x) = 1 - (1 - x) = 1 - 1 + x = x
It's clear that f(x) does not yield the same result as f(1 - x). Eliminate A.
Now for option B:
f(x) = 1 - x^2
f(1 - x) = 1 - (1 - x)^2 = 1 - (1 - 2x + x^2) = 2x - x^2
Again, there's no match between f(x) and f(1 - x)
Try the others... you should see why D is the correct answer.
Wierd Problem
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