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If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.
On the other hand, the inverse image or preimage under f of an element y of the codomain Y is the set of all elements of the domain X whose images under f equal y. [6] In symbols, the preimage of y is denoted by f − 1 ( y ) {\displaystyle f^{-1}(y)} and is given by the equation