## Posts Tagged ‘Domain’

## Problem 671

For the pair of function f and g, determine the domain of f/g.

F(x) = ,g(x) = 4-x

**Solution:-**

The domain of t/g is the set of all values common to the domains of t and g, excluding values for which g(x) is 0.

The domain of a function defined by an equation is the set of all number for which real values of the function can be calculated. A function can be undefined at a number because calculating its value results in an undefined in an undefined operation like division by zero or an even root of a negative number.

For the function , f(x) =. The denominator is zero for x= 3, which result in an undefined value. Therefore, the domain of f is {x I x is a real number and x3}.

For the function , g(x) = 4 – x, a value can be calculated for any real number x. Therefore, the domain of g is {x I x is a real number}.

The domain of the quotient also excludes all values for which f(x) is zero. Therefore solve the equation

4 – x = 0.

X = 4

The domain of f/g is the set of all values common to { x I x is a real number and x 3} and {x I x is a real number}, and also excluding x = 4.

Therefore , the domain of f/g is {x I x is a real number and x 3 and x 4}.

## Find domain and range

**Find domain and range**

For every relation, there are two important sets of elements called the *domain *and *range*.

**Domain and Range**

** **

In a relation, the set of all values of the independent variable (*x*) is the **domain. **The set of all values of the dependent variable ( *y*) is the **range.**

**Example**

{(**3**, 2**1**), (**4**, **2**), (**4**, **5**), (**6**, **8**)}

The domain, the set of *x*-values, is {**3**, **4**, **6**}; the range, the set of *y*-values, is {2**1**, **2**, **5**, **8**}. This relation is not a function because the same *x*-value 4 is paired with two different *y*-values, 2 and 5.

## What is relation and types of relations

**What is relation (Mathematics) and types of relations:-**

Relation (mathematics) is same as in real life, it is define as two things connected to each other or it is the property of things to connect in a certain manner.

Example:

- Akbar was the son of Humayun
- 25 is the multiple of 5.
- In a triangle ABC, AB is the base.

**Domain and Range of a Relation:** If R is a relation defined between set A and set B then set of first elements of ordered pair is known as Domain and set of second elements of the ordered pair is known as Range means Domain of R is {a|(a,b) є R} and Range of R is {b|(a,b) є R}.

Example :

If R = { (1,2),(1,4),(1,6),(2,2),(2,4),(2,6)} ( A relation between A and B )

So Domain of R = {1, 2} = A and Range of R = {2,4,6} = B

**Types of Relation:-**

**1.**** Reflexive Relation:** If every element of a set A is related to itself In a Relation R it means that Relations R is reflexive relation.

(a,a) є R for all a є A.

2. **Symmetric Relation:** A relation R defined in a set A, if element ‘a’ is related to ‘b’ and ‘b’ is also related to ‘a’ in the same way then this relation is known as Symmetric Relation.

Relation R is symmetric if (a,b) є R => (b,a) є R for all a,b є A.

**3.** **Anti symmetric Relation:** A relation R defined in a set A. if element ‘a’ is related to ‘b’ and ‘b’ is related to ‘a’, both will be true only when a=b, then this relation is known as anti symmetric Relation.

(a,b) є R and (b,a) є R => a = b, for all a,b, є A

**4.** **Transitive Relation:** A relation R defined in a set A, if element ‘a’ is related to ‘b’ and ‘b’ is related to element ‘c’ from this if ‘a’ has relation to c then this relation is known as Transitive relation.

If (a,b)є R and (b,c)є R => (a,c)єR , for all a,b,c, є A

**5.** **Equivalence Relation: **we call equivalence relation to a Relation R if

R is reflexive

R is Symmetric

R is Transitive

**6.** **Partial order Relation:** we call Partial order relation to a Relation R if

R is reflexive

R is Anti Symmetric

R is Transitive

**7.** **Total order Relation:** we call Partial order relation to a Relation R if

R is Partial Order relation

And for every a,b є A either (a,b) є R or (b,a) є R or a = b are true.