1. Find all functions $f: \mathbf{R} \rightarrow \mathbf{R}$, such that for any real numbers $x, y$, we have
$$
f\left(x^{2}\right) f\left(y^{2}\right)+|x| f\left(-x y^{2}\right)=3|y| f\left(x^{2} y\right) \text {. }
$$