Question 177
Determine all functions $f: \mathbb{R} \setminus \{0\} \to \mathbb{R} \setminus \{0\}$ such that
$$
f\left(x^{2} y f(x)\right)+f(1)=x^{2} f(x)+f(y)
$$
holds for all nonzero real numbers $x$ and $y$.
$$
f\left(x^{2} y f(x)\right)+f(1)=x^{2} f(x)+f(y)
$$
holds for all nonzero real numbers $x$ and $y$.