Question 65
A polynomial $f(x)$ with real coefficients is called generating, if for each polynomial $\varphi(x)$ with real coefficients there exists positive integer $k$ and polynomials $g_1(x), \dots, g_k(x)$ such that
$$
\varphi(x) = f(g_1(x)) + \dots + f(g_k(x)).
$$
Find all generating polynomials.
$$
\varphi(x) = f(g_1(x)) + \dots + f(g_k(x)).
$$
Find all generating polynomials.