My teacher said that the polynomial function such that $\displaystyle f(x)f\left(\frac{1}{x}\right)=f\left(x \right )+f\left(\frac{1}{x} \right )$ exists and that must be of the form $\displaystyle f(x)=1 \pm x^n$. But he didnt give any proof. Can anyone help me with a proof that the function satisfying the above condition can only be $\displaystyle f(x)=1 \pm x^n$