Question 119
Both $f(x)$ and $g(x)$ are polynomials with real coefficients, and are not identically zero. Suppose that they satisfy the following functional equation:
$$
f(x^3) + g(x) = f(x) + x^5g(x)
$$
Give an example of such a function $f(x)$ with the smallest possible degree.
$$
f(x^3) + g(x) = f(x) + x^5g(x)
$$
Give an example of such a function $f(x)$ with the smallest possible degree.