Concept guide
Inverse functions: exchanging a finite bijection table and inverting an affine map with nonzero slope
(1) A={1,2,3}, B={4,5,6}, p(1)=5, p(2)=6, p(3)=4. First confirm that p is a bijection, then exchange its ordered pairs to get a candidate q, validate q as a total function B→A, and check q(p(x))=x and p(q(y))=y separately. (2) f:ℝ→ℝ, f(x)=−4x+6 (m=−4≠0): find the inverse g(y)=uy+v with u, v reduced rationals with positive denominators, and verify both identities for all reals. (3) Show that the exchanged table of h(1)=4, h(2)=4, h(3)=6 is not a function B→A, and that f^{-1} is not 1/f.