Question 115
Determine all non-negative real-valued functions $f$ defined for non-negative real numbers, which satisfy
$$
f(x^2) + f(y) = f(x^2 + y + x f(4y))
$$
for every pair of non-negative real numbers $x$ and $y$.
$$
f(x^2) + f(y) = f(x^2 + y + x f(4y))
$$
for every pair of non-negative real numbers $x$ and $y$.