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I have been reading about metric spaces and came across an elementary property that I am having difficulty proving. A quick search on these forums and google has also failed.

Given a metric space with distance function [itex]d[/itex], and an increasing, concave function [itex]f:\mathbb{R} \rightarrow \mathbb{R}[/itex] so that [itex]f(0)=0[/itex], show that [itex]f\circ d[/itex] is a metric.

Of course, only the triangle inequality is nontrivial.