Question 119
Determine all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying
$$
f(f(x)f(y) + f(y)f(z) + f(z)f(x)) = f(x) + f(y) + f(z)
$$
for all real numbers $x, y, z$.
$$
f(f(x)f(y) + f(y)f(z) + f(z)f(x)) = f(x) + f(y) + f(z)
$$
for all real numbers $x, y, z$.