Note on Linear Functions

Linear Function is defined as follows, considering two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B.

When a relation satisfies this rule, it is called a fuction.

In this chapter, we will study how a function is a relation, but a relation may not be a function.

Hence the function calculator sections helps to differentiate relation and a function.

Characteristics of Functions

1. Two functions f,g are equal if and only if they have same domain and range and f(x)=g(x) for every x ? A. This will also help us on linear equation form

2. f: A ---> B is one-one(Injection) if and only if for all a0 ,a1 ? A, “f(a0)=f(a1) implies that a0=a1 “

3. f: A ---> B is onto(Surjection) if and only if f(A)=B. also for every b ? B, there exists an element a ? A such that f(a)=b.

4. f: A ---> B is Bijection if f is one-one and f is onto.then number of elements in A is equal to number of elements in B.