SEC2_GYM · Functions · FUNC.COMPOSITION.INVERSE

Composition and inverse functions

Intuition

Understand first, compress later.

A function maps inputs to outputs. Table, formula and graph tell the same relationship in different languages.

Switch representations

Mapping between two setsf: A → B — neither injective nor surjective

domain Acodomain Bthe assignment fnot hit

Every element of A has exactly one arrow leaving it — that is what makes f a function. Two elements of A are sent to the same element of B (2 and 3 ↦ b), so f is not injective. Nothing maps onto c, d in B, so f is not surjective.

Formal view

You can composition and inverse functions when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.