functional equation (conti-function $f(x)$)

Question

I would appreciate if somebody could help me with the following problem

Q: Find conti-function $f(x)=?$ $$4(1-x)^{2} f \left({1-x\over 2} \right)+16f \left({1+x\over 2} \right)=16(1-x)-(1-x)^{4}$$

Answer 1

Change $x$ to $-x$ and then solve it as a system of two equations for the unknown $f$ values.

EDIT

As noted by Blatter, below,

We end up with $f(x)=x^2-1$ or $f(x)=1-x^2$

only $f(x)=1-x^2$ works in the original equation!