The answer to this question is C. Only F(x) = 2 - x - x2 satisfies the function when f(1-x) = f (2+x) for all x. The easiest way to solve this equation and find the right answer is to begin substituting real numbers in place of x. Since f(1-x)= f (2+x) is true for all x, then it allows you to plug any number in for x and you will be able to find the correct answer.
In order to use this technique, it is simplest to try to plug in smaller numbers first like 0 or 1. If you try to plug in larger numbers, you will still get the right answer, but likely will have to do more work than is necessary.
Since f(1-x)= f (2+x) is true for all x, the best way to solve this type of question is to plug in some real number. When x = 0, f (1-0) = f (2+0) => f (1) = f (2).
Then evaluate all the formulas for x=1 and x=2. The formula that gives you the same answer for both is the right one.
After calculation, we can know C is the right answer.