# Knowledge of the definitional domain and value domain of a function

### What are the domain of definition and domain of value?

The range of values of a function’s independent variable (e.g., x) is the function’s domain of definition; the range of values of a function’s dependent variable is the function’s domain of value. Definition and value range is for “function”: in a certain process of change, two variables x, y, for each value of x, y has a unique value and it corresponds to, y is a function of x. This relationship is generally used in y = f (x), y = f (y), y = f (y), y = f (y), y = f (y), y = f (y). This relationship is generally expressed by y = f (x). Where x is called the independent variable and y is called the dependent variable.

Finding the domain of definition of a function:

1. The domain of definition of a function is the set of values taken by the independent variables of the function, which is generally required to be expressed in terms of sets or intervals.

2, a common question is the definition of the domain from the analytic formula, this time to recognize the independent variable, followed by the examination of the location of the independent variable, the location determines the range of the independent variable, and finally the problem of finding the definition of the domain of the problem is reduced to solving the problem of the set of inequalities.

3, the composite function y = f of the definition of the domain, should be y = f (u) to find the range of u, that is, the range of g (x), and then from the range of x I1; and then by the g (x) to find the definition of y = g (x) of the domain of I2, the intersection of I1 and I2 that is the composite function of the definition of the domain.

4. The domain of definition of a segmented function is the concatenation of the intervals.

5, containing parameters of the function of the definition of the domain of the parameter needs to be categorized to discuss the parameters, if the parameters in different ranges of the definition of the domain is not the same, then in the description of the conclusion of the separate instructions.

6, the definition of the domain sometimes need to classify the independent variables to discuss, but in the description of the conclusions need to be classified to find the various sets of sets of concatenation, as the function of the definition of the domain.

### What is the value domain? What is the domain of definition?

Domain of value is in the classical definition of a function, the range of values changed due to a change in the variable is called the domain of the function, in the modern definition of a function is the set of all elements in the domain of the definition of all the elephants corresponding to a corresponding law under the set of all the elephants. For example, if f(x)=x, then the range of values of f(x) is the domain of the function f(x).

The domain of definition (domainofdefinition) refers to the range of values of the independent variable x, is a function of one of the three elements (definition, value, corresponding to the law), corresponding to the object of the law. To find the function of the domain of definition mainly includes three types of questions: abstract function, general function, function application.

Extended information:

Solving a math problem by looking at an equation as a whole and replacing it with a variable that simplifies the problem is called commutative. The essence of permutation is transformation, the key is to construct the element and set up the element, the theoretical basis is the equivalent substitution, the purpose is to change the object of study, the problem will be moved to the new object of the knowledge background to study, so as to make the non-standard type of problem standardization, complex problems simplified, and become easy to deal with.

The permutation method is also known as the auxiliary element method and the variable substitution method. Through the introduction of new variables, you can link the scattered conditions, implicit conditions revealed, or link the conditions with the conclusion. Or change into a familiar form to simplify complex calculations and inferences.

### What is the domain of definition and domain of value

Question 1: The difference between the domain of value and the domain of definition, in detail, preferably with examples The domain of definition is the range of values of the independent variable The domain of value is the range of values of the dependent variable

For example, we often use x to represent a function of y

Then the range of values of x is the domain of definition

The range of values of y relates to the independent variable x, the range of y is the domain of value

Question 2: What do the definitional domain, domain of value, and upper domain mean in linear algebra? Understanding of definitions can be deepened based on different examples.

Definitional domain: is the range of values of the independent variable in a function that makes sense or is artificially specified, e.g., y=√x definitional domain is x>=0, because x=0, x is not equal to 0, and of course there are composite cases of these simple forms.

value domain: the function y = f (x) of the range of values is the value domain, according to the type of function or the definition of the domain of the different ways to find the value domain is also different. For example, the value range of y=sinx is [-1, 1].

Upper domain: let f:A—–>B for a mapping, A is called the definition of this mapping domain (domain), B is called the mapping of the accompanying domain (codomain) (or on the domain, the arrival domain), f(A)={f(a)|a belongs to A} is called the mapping of the image of the domain (if the elements of the B has a value of concepts (for example, B is the set of real numbers), also known as the value of the domain). , also called the domain of values). Clearly there is f(A) that is a subset of B.

Question 3: What is the difference between the domain of definition and the domain of value of y = x + 1 The domain of definition is R, as is the domain of value.

While they have the same domain of definition and the same domain of value, x = 2 and y = 2 do not have the same meaning.

Because x=2 corresponds to y=3,y=2 corresponds to x=1.That is, given a value of x, you will always get y one larger than x.

Question 4: What is the quadratic function, the domain of definition, and the domain of value?

Question 5: What is the difference between the domain of definition and the domain of value The domain of definition refers to the range of values of the independent variable.

Domain of value refers to the range of values that change as a result of a change in the variable is called the domain of the function

Question 6: What does domain of definition mean? The definition domain is the range of values of an unknown number symbols are () [ ] two kinds. The first one is excluding the values on both sides. The second is inclusive and can be mixed