Is it something to do with eigenvalues? Like Ax is an eigenvector of A or something? Or is it that Ax is equal to $\displaystyle -(Ax \cdot x) $? If that's the case, wouldn't that make the original equation be $\displaystyle f(x) = (-(Ax \cdot x) \cdot x) e^{||x||^{2}}$? Wouldn't that make it a scalar being on one side of the dot product and a vector on the other? This wouldn't work.