MAPPING AND FUNCTION

A Set is defined as a collection of objects, things or numbers. Given two non-empty sets **A **and**B**.What then is Mapping?If there is a rule, which assigns an element **xA**, a unique element **yꞒB**, then such a rule is called Mapping. The set **A **is called the Domain of the mapping while the set **B **is called the co-domain of the mapping. If the rule which associates each element **xꞒA**, a unique element **yꞒB**is denoted by **f**, the mapping between the set **A **and the set **B **can be represented by f : A**B**

**f (x) = y **where** y** is unique element in **B **which corresponds to the element **x **in **A.**

The element **y** in **B** is called the image of **xꞒA**. A Subset of the co-domain, which is collection of all images of the elements of the domain is called Range.

Example 1.

Let X = {N, C, G} where N, C and G represent the countries Nigeria, Cameroun and Ghana respectively. Let Y = {a, b, y, k, n} where a, b, y, k and n represent Accra, Abuja, Younde, Kinshasha and Nairobi respectively, and let the mapping **f** from the set **X** into the set **Y **be “the mapping** f** from the set **X **into the set**Y**Solution.Set **X** is the domain, while the set **Y **is the co-domain. Set{y, a, b} is the imageAlso, f (N) = b, f (C) = y and f (G) = a.

Example 2: Page 74 in the textbook(Ref)Let **g**assign to every country of West Africa its capital city. The domain of **g** is the set of countries in West Africa while the co-domain is the set of capital cities in West Africa. The image of Nigeria is Abuja while the image of Ghana is Accra.

Solutiong (Nigeria) = Abujag (Ghana) = Accra

Function: A function is a mapping whose co-domain are set of numbers (integers)

Example 6: page 75 in the textbook. (Ref)

Solution.ɸ (1) = 5, ɸ (2) = 9, ɸ (3) = 13, ɸ (4) = 17

**·˙ ·**ɸ (a) = 4a + 1.

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