Concept guide
Surjectivity and codomain coverage: range, preimages and changing the codomain
Let A={1,2,3,4,5}, B={1,2,3} and the function table f: (1,2),(2,1),(3,3),(4,2),(5,1). Confirm f is a total function A→B, find the range f[A] and the preimages, decide whether f is surjective and find the first preimage of t=2; then replace the codomain by B2={1,2,3,4} and by B3={1,2}, deciding legality and surjectivity; finally treat ∅→∅ and ∅→{7}.