Okay, so you need to check if f(x) = f(1-x)

Let's do this one by one.

Case A: - Wrong
\(f(x) = 1-x\)
\(f(1-x) = 1-(1-x) = x\)

So we clearly see that f(x) is not f(1-x)

Case B: Wrong

\(f(x) = 1-x-x^2\)
\(f(1-x) = 1-(1-x)-(1-x)^2 = x - 1 - x^2 + 2x = 3x-1-x^2\)

Case C: Wrong

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

Case D: Right

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

Let's check E just to be sure.

Case E: Wrong

\(f(x) = \frac{x}{1-x}\)
\(f(1-x) = \frac{1-x}{1-(1-x)}=\frac{1-x}{x}\)

Answer: D