Denominator is not zero; The number of even roots is non-negative; The real part of logarithm is greater than 0; The base of exponent and logarithm is greater than 0 and not equal to1; Y = x≠kπ+π/2 in y=tanx。 Y = x≠kπ in y=cotx, etc. The range is the value range of y in the function y=f(x).

Common methods of evaluating domain: reduction; Mirror image method (number-shape combination method), function monotonicity method, collocation method, method of substitution, inverse function method (inverse method), discriminant method, compound function method, triangle method of substitution method, basic inequality method, etc.

What are the areas of definition and value?

Domain refers to the value range of independent variables; Range refers to the value range of the dependent variable. Independent variable refers to the factors or conditions that researchers actively manipulate and cause the dependent variable to change, so independent variable is regarded as the cause of the dependent variable.

Dependent variable (dependent variable) is a technical term in function. In a functional relationship, some specific numbers will change with the change of another (or several other) numbers, and this change is called dependent variable.

Definition domain and its representation in the function y=f(x), the definition domain refers to the "set" (or "interval") formed by all the values of the independent variable x, and the definition domain should be expressed in the form of set or interval. When the number of values of x in the definition domain is limited, it can not be expressed in interval form, but only in set form.

Data expansion

Function, a mathematical term. Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping.

The modern definition of a function is to give a number set A, assume that the element in it is X, apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B, assume that the element in B is Y, and the equivalent relationship between Y and X can be expressed as y=f(x). The concept of a function includes three elements: the domain A, the domain B and the corresponding rule F, among which the core is the corresponding rule F, which is the essential feature of the function relationship.