Ch. 3. Functions - Concept Review

Function – definition

Let A and B be two non-empty sets. Then a function ‘f’ from set A to set B is a rule or method or correspondence which associates elements of set A to elements of set B such that

(i) all elements of set A are associated to elements in set B.
(ii) an element of set A is associated to a unique element in set B.


Domain, Co-Domain and Range of a Function

Let f: A → B. Then, the set A is known as the domain of f and the set B is known as the co-domain of f.

The set of f-images of elements of A (elements in set B associated with elements in set A) is known as the range of f or image set of A under f and is denoted by f(A)

Thus range of f = f(A) = {f(x): x Є A}

F(A) is a subset of B.

Range of f is a subset of co-domain of f.


Number of functions

Let A and B be two finite sets having m and n elements.
The total number of functions from A to B is n^m.


Types of functions

1. Even and odd functions

2. Monotonic functions

3. Step function

4. Modulus function

5. Algebraic function

6.Exponential function

7. Logarithmic function

8. Inverse function

9. composite function

10. Trigonometric function