Question 124
Find all functions $f: \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers, such that
$$
f(x)f(yf(x)-1) = x^2f(y) - f(x) \quad \text{for all } x, y \in \mathbb{R}.
$$
$$
f(x)f(yf(x)-1) = x^2f(y) - f(x) \quad \text{for all } x, y \in \mathbb{R}.
$$