Functions question - what's your approach?

[doclkk]

For which of the following functions f 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)

(D)

I picked #'s. X = 2. So I try to discover when F(2) = F(-1).

But I think this method is really slow. Took me like 2:45.

So how do you set up your table. Do you set up a table of 2 and a table of -1.

And just go one by one?

Because that would be a total of 6 equations ... at a minimum right? Are there ones that you can immediately eliminate.

[sreak1089]

I don't pick numkbers here. My idea is to substitute 1-x inplace of x and see if it results in the same function. Looking at A, B, E, they don't look likely. Try subsituting 1-x inplace of x in C and D and you will find that the right answer is D.

[sreak1089]

Let me clarify:

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

f(1-x) => substitute x == 1-x in the above function
and you have (1-x)^2*(1-(1-x)) = (1-x)^2*(1-1+x)^2 = (1-x)^2*x^2