Question 1126968
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In Math,  there is  NO  such term and such notion  (such commonly acceptable term and/or notion in Math)  as  "comprehensive function".



It exists only in your imagination. 



More precisely,  it is you who think that this term exists - and practically nobody else.



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For relevant terminology,  see this Wikipedia article


https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection