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Can one function feed another?

Can one function feed another? · Diagrams

Composition maps into reached subsets

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x in Dg=Dfg passes through g into a subset of Df, then f into a subset of Rf. The direct fg arrow reaches the same output; full outer sets remain distinct from reached subsets.
x in Dg=Dfg passes through g into a subset of Df, then f into a subset of Rf. The direct fg arrow reaches the same output; full outer sets remain distinct from reached subsets.
x in Dg=Dfg passes through g into a subset of Df, then f into a subset of Rf. The direct fg arrow reaches the same output; full outer sets remain distinct from reached subsets.
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