I am studying basic concepts of metrics. and I ve been practicing axioms of metrics to prove some functions can be metrics or not. then this question showed up and I do not understand what am I being asked for. how is related to axioms of metric? am i supposed to find a function?

$X=\{a,b,c\}$ and $(\alpha ,\beta)\in R^2$. Define $d_{\alpha\beta}$ as a function on $X\times X$ such that $d_{\alpha\beta}(a,b)=1$ and $d_{\alpha\beta}(b,c)=\alpha$ and $d_{\alpha\beta}(c,a)=\beta$. Find all possible $(\alpha,\beta) $ s.t $d_{\alpha\beta}$ is a metric.

Categories