6

Part of 1985 Federal Competition For Advanced Students, P2

Problems(1)

Source: Austria 1985

Find all functions

f: \mathbb{R} \rightarrow \mathbb{R}

satisfying: x^2 f(x)\plus{}f(1\minus{}x)\equal{}2x\minus{}x^4 for all

x \in \mathbb{R}

functionalgebra proposedalgebra