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 **R _{f }**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**.

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