Suppose (X,d) is a metric space and φ:[0,∞)→R is an increasing function such that φ(t)≥0 for all t and φ(t)=0 if and only if t=0. Also suppose φ is subadditive, that is, φ(s+t)≤φ(s)+φ(t). Show that with d′(x,y):=φ(d(x,y)), we obtain a new metric space (X,d′).