Question: Let g be a continuous strictly increasing function on the Reals. g(0) = 0. For every such g and every undirected graph G with positive

Let g be a continuous strictly increasing function on the Reals. g(0) = 0. For every such g and every undirected graph G with positive or zero-valued edge weights w, prove or disprove that a path from vertex v0 to vertex vk is a shortest path on G with weights w if and only if it is the shortest path on G with weights g(w).?

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