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# what is this question asking for? basic metric concepts

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.