(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Make [; f: A \rightarrow B ;], [; g: C \rightarrow D ;], [; h: E \rightarrow F ;] functions in which [; \text{Im} f \subseteq C;] and [; \text{Im} g \subseteq E;]. Show that [; f \circ ( g \circ h ) ;] and [; h \circ ( g \circ f ) ;] are valid if, and only if, [; f \circ ( g \circ h ) = h \circ ( g \circ f) ;].

2. Relevant equations

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3. The attempt at a solution

Though the proof seems to be very trivial, I couldn't see very deeply.

I set the propositions necessary for the functions to exist, but I couldn't find a relation in the images, domains and codomains to make them equal.

Thanks

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# Homework Help: Function composition

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