INVERSE OF MAPPING

INVERSE OF MAPPING

Consider the function, f(x) = 2x + 3 on the set A = {-2, 1, 3} into set B = {-1, 5, 9}. The function f takes an element from the set A to produce a unique image in the set B. Alternatively, the function f can be defined as the set {(-2, 1), (1, 5) (-1, 5) (3, 9)}. i.e f {(-2, 1), (1, 5) (-1, 5) (3, 9)}. Suppose we consider the relation which reverses the operation of associating an element from the set A, a unique element in the set B. Let the relation g associate with every element in B a unique element in A. The relation g can be defined as the set of the ordered pairs g = {(-1, -2) (5, 1) (9, 3)}. The relation g is a mapping it is called the inverse of the function f and it is usually denoted by f^-1                                                                                                   Note: A function has f has an inverse, if it is both one-one and unto

Summary.

1. A mapping is a rule which assigns an element xꞒX a unique element yꞒY.
2. In the mapping f : X→ X the set X is called the domain, while the set Y is called the co-domain.
3. The range is a subset of the co-domain which consist of all the images in the domain.
4. A function is mapping whose co-domain is the set of the numbers.
5. For a relation to be a mapping or function, the following condition must ne satisfied
6. Each element of the domain has an image in the co-domain.
7. Every element of the domain has a unique image.
8. The mapping f : X → Y is said to be an unto mapping if every element of the co-domain is an image of at least one element in the domain.
9. In an unto mapping, the range is equal to the co-domain.