TYPES OF MAPPING WITH EXAMPLES.
1. One – One Mapping.Let f: X→ Ybe a mapping that establishes the correspondence between the sets X and Y. The mapping f is called a one – one mapping, if different elements in the domain X have different elements in the co-domain Y. Example: The mapping which associates each state in Nigeria with its Governor is a one – one mapping.
2. Onto– Mapping.Let f : X→ Y be a mapping from the set X to the set Y. The mapping f is called an onto – mappingif every element of the co-domain is an image of at least one element in the domain. Every member of the co-domain is at least one member of the domain, the range of an onto mapping is equal to the co-domain.
3. Identity Mapping.Let fі : X→ X be a mapping defined by fi (x) = x for all xꞒX, then fi is called an identity mapping. It is a mapping which takes an element unto itself.
4. Constant Mapping.Let fi : X→ Y be a mapping defined by fi (x) = x for all xꞒX, then fi is called a constant mapping, if for every xꞒX, f(x) = K where K is a constant. The range of Rf of a constant mapping consists of one element.
5. Composite Mapping.Let fi : X→ Zand g : Z → Ybe two mappings such that the co-domain of f is the domain of g.XZY. The mapping f takes an element in X and produces an image in Z and produces an image in Y. The mapping gof takes an element in X and produces an image in Y.