# Mathematics lesson, subject of functions. Concept of domain, codomain and range in functions. What is function. Relations and functions. The definition of function.

Definition Of Function

Let we take non-empty set of A and B.

The relation that mapping up least and most 1 time each elements of set A to elements of set B is called function.

There is two important rule in a function.

1-Each element of set A (is domain) must maps to with an element of set B(is codomain).

2- An element of set A (is domain) must maps to with an element of set B (is codomain) most 1 time.

A function from A to B is shown as

f: A → B

Or Domain set of A Function

In a function from A to B the A set is called set of domain or set of value.

Codomain set of A function

In a function from A to B the B set is called the set of codomain or the set of definition.

The Range Set of A Function

In the B set, the elements that matches with the elements of set A is create a set. This set is called range set or image set.

The Relationship of A function

A relation that pairs the elements of set A to elements of set B is called the relationship of function.

Relationship is shown with arrow or mathematical formula.

Example:

A f(x) function is given in the following.

f(x) = 3x + 1

The name of this function is f.

The input of this function is "x".

The output of this function is "3x + 1".

There is the relationship "x → 3x + 1" in this function.

The function output for x = 2,

f(2 ) = 3*2 + 1 = 7 dir.

The function output for x = 5

f(5) = 3*5 + 1 = 16

The function output for x = 8

f(8) = 3*8 + 1 = 25

The functions can be defined in various form simple or mixed.

Defining Functions with Finite Sets

It is seen a function from A to B in the following. Example

In the following in the example is shown that the elements of the set A to pair with the elements of set B.

It is not a function. Because, all elements (c, d) of the set A is not mapping with an element of set B. Example:

In the following in the example is shown that the elements of the set A to pair with the elements of set B.

It is not a function. Because, an element(is d) of the set A matched with element of set B more than once. Example:

It is a function. Because, each elements of the set A matched with element of set B at least and most 1 times. Example:

A and B sets is given,

A = {2, 3, 5, 6}

B = Whole Numbers

f(x) : A → B

f(x) = 5x + 2

Find the image(range) set of the function.

Solution:

The elements of the range set can shown in the following form

R = {b1, b2, b3, b4}

b1 = 5.2 + 2 = 12

b2 = 5.3 + 2 = 17

b3 = 5.5+2 = 27

b4 = 5.6 + 2 = 32

R = {12, 17, 27, 32}

Also, the range set (R) can also shown in "f(A)" form.

R = f(A)

Example:

f: A → B

f(x) = 3x + 6

f(A) = {12, 18, 24, 33}

Find elements of the set A

Solution:

Elements of the set A must matches up at most and least 1 time with elements of the set B.

A = {a1, a2, a3, a4}

3*a1 + 6 = 12

3*a1 = 6

a1 = 2

3*a2 + 6 = 18

3*a2 = 12

a2 = 4

3*a3 + 6 = 24

3*a3 = 18

a3 = 6

3*a4 + 6 = 33

3*a4 = 27

a4 = 9

Let we write the set A.

A = {2, 4, 6, 9}

Compound Functions

RISE KNOWLEDGE

11/08/2018

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