# Interval representation of the domain of definition of a function

### Express the domain of definition of the function in terms of an interval as ________.

(-∞, -1) ∪ (-1, 0]

The function’s domain of definition is: {x|},

Solve for x ≤ 0 and x ≠ -1,

so the answer is: (-∞, -1) ∪ (-1, 0].

### What is the definitional domain of a function expressed in terms of an interval

a<x<b is expressed in terms of an interval as (a,b)a≤x≤b is expressed in terms of an interval as [a,b]a<x≤b is expressed in terms of an interval as (a,b]a≤x<b is expressed in terms of an interval as [a,b)x∈R, and x≠0, is expressed in terms of an interval as (-∞, 0)∪(0,+∞)a& lt;x<b, and x≠c(a<c<b), that is, a<x<c, and c<x<b so in terms of intervals it is (a,c)∪(c,b) and so on

### Definition of the domain of representation

The definition of the domain of a function is represented by three methods: inequalities, intervals, and sets. Finding the domain of definition of a function consists of three main types of questions: abstract functions, general functions, and function application questions. Meaning is the range of values of the independent variable x. Extended information

function definition domain is one of the three elements of the function (definition domain, value domain, corresponding law), corresponding to the object of the law. It refers to the range of values of the function’s independent variable, that is, for two non-empty sets D, M that have a functional correspondence, any number in the set D, there is and only a definite number in the set M with which it corresponds, then the set D is known as the function definition domain.

Representation of the domain

The domain of a function is represented by inequalities, intervals, and sets. Finding the domain of a function consists of three main types of questions: abstract function, general function, function application questions. Meaning is the range of values of the independent variable x.

The domain of definition of a function is defined according to the problem that the function is to solve, the function`s domain of definition is generally defined in three ways

(1) the natural domain of definition, if the function of the corresponding relationship has an analytic expression to represent, then the range of values of the independent variable to make the analytic formula meaningful is called the natural domain of definition. For example, the function, to make sense of the analytic expression of the function, then, therefore, the natural domain of definition of the function is;

(2) function has a specific application of the practical context. For example, the function represents the relationship between speed and time, in order to make sense of the physical problem, then the time, so the function’s domain of definition is;

(3) artificially defined domain of definition. For example, in the study of a function, only examine the function of the independent variables in the [0,10] range of a section of the functional relationship, and therefore the definition of the function is defined as the definition of the domain of [0,10].

### What are the various representations of the domain of definition of a function?

For a function, the domainofdefinition is a set that is one of the three elements of a function (domain of definition, domain of values, and law of correspondence).

The domain of definition is the range of values of a given variable.

It is sufficient to represent the domain of definition by the representation of a set.

A, enumeration: commonly used in the representation of finite sets, the set of all elements one by one, written in curly brackets. Such as {1,2,3,……}

B. Descriptive method: commonly used to represent infinite sets, the common attributes of the elements of the set described in words, symbols or formulas, etc., written in curly brackets. Such as {x|x<3}

C, expressed in intervals, such as [3,5]

In practice, the descriptive method and the interval method is used more.

### Find the domain of definition of the function in terms of intervals (to process)

x²-5>0,

x<-√5, orx>√5.

Definition of the domain (-∞, -√5) ∪ (√5, +∞).

### Does the domain of definition of a function have to be represented by an interval?

The domain of definition can be expressed in terms of sets or in terms of intervals, but not in terms of inequalities.

It is OK to represent the domain of definition by a set of descriptors, it is wrong to use inequalities, which can be used to represent the range of values of x, and cannot be called the domain of definition.