16. (1994 IMO Shortlist Adaptation) Let $\mathbf{R}^{+}$ be the set of all positive real numbers. $\alpha, \beta$ are given non-zero real numbers. Find all functions $f: \mathbf{R}^{+} \rightarrow \mathbf{R}$, such that for all $x$ and $y$ in $\mathbf{R}^{\prime}$, we have $f(x) f(y) \geqslant \frac{y^{\rho}}{x^{0}+x^{\beta}}[f(x)]^{2}+\frac{x^{\beta}}{y^{\alpha}+y^{\beta}}[f(y)]^{2}$.