MAPPING AND FUNCTION                                                  

A Set is defined as a collection of objects, things or numbers. Given two non-empty sets A andB.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 yꞒBis denoted by f, the mapping between the set A and the set B can be represented by f : AB

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 setYSolution.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 gassign 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.