Question 7
Let $f: \mathbb{R} \to \mathbb{R}$ and let:
$$
f(f(x)+f(y))+f(f(x)-f(y)) = x^k f(x) + y^k f(y)
$$
hold, where $k$ is a given natural number. What values can $f(1)$ have? (easier case: $k=2$).
$$
f(f(x)+f(y))+f(f(x)-f(y)) = x^k f(x) + y^k f(y)
$$
hold, where $k$ is a given natural number. What values can $f(1)$ have? (easier case: $k=2$).