What does it mean to have a definition in a function of high numbers?

It's this function that makes sense within this defined domain.

If A is BInverse functions, then b is a direct function of a; And vice versa, because a and b are inverses of each other, i.e., b is also an inverse of a, so a is a direct function of b.

For example, if y=arcsinx is the inverse of x=sny, then x=siny is a direct function of y=arcsinx.

x=siny is also the inverse of y=arcsinx, so y=arcsinx is a direct function of x=sny.

Traditional Definition:

In general, in the process of a noisy slippery change, suppose there are two tremor variables x and y, and if there is a uniquely determined y corresponding to any x, then x is said to be an independent variable.

y is a function of x. The range of values of x is called the domain of the function.

The range of values for the corresponding y is called the range of the function.

element:

The set of input values x is called the defined domain of f; The set of possible output values y is called the range of f. The domain of a function is the set of actual output values obtained by mapping f to all elements in the defined domain. Note that it is incorrect to call the corresponding domain a value range, and the value range of a function is a subset of the corresponding domain of the function.

Computer science.

, the data type of the parameter and the return value.

The defined domain and the corresponding domain of the sub-program were determined, respectively. Therefore, defining the domain and the corresponding domain is a mandatory constraint that is determined at the beginning of the function. On the other hand, the range is related to the actual implementation.

For the above content, please refer to Encyclopedia - Functions.

The theoretical explanation is that in the neighborhood of x0, for any x, f(x) has a corresponding value, and there is no part in the middle. But in other words, it means that you don't consider other factors around x0 and just look at the point of x0.

That is, one of the neighbors of x0 is within the defined domain of f(x).

For example, f(x)=x, then the neighborhood of the point x=2 is in the domain defined by f(x)=x, then f(x)=x is defined in a neighborhood of x=2.

G(x)=x, and at x=0 any neighborhood is not exactly in the defined domain of g(x), so it cannot be said that g(x)= x has a definition in a certain neighborhood at x=0.

The high school function is defined as follows:

Let a and b be two sets of non-empty numbers, and if, according to some definite correspondence f, there is a uniquely definite number f(x) corresponding to any number x in set a, then f:a b is called a function of set a to set b. denote y=f(x),x a.

I feel that f(x) appears very abruptly!! I think it's better to follow the following definition:

Let a and b be two sets of non-empty numbers, and if, according to some definite correspondence f, there is a uniquely definite number y corresponding to any number x in set a, then f:a b is a function of set a to set b. denote y=f(x),x a.

In this way, it feels natural for f(x) to appear.

Function is an important mathematical model to describe the law of change in the objective world.

In high school, as in compulsory education, functions are not only regarded as dependencies between variables, but also used sets and corresponding languages to describe functions. Students will learn specific basic elementary functions such as exponential functions and logarithmic functions, experience the process and methods of using function concepts to build models in combination with practical problems, realize that functions are the foundation of mathematics and other disciplines, and be able to initially use function ideas to understand and deal with simple problems in real life and society. In order to strengthen the organic connection between different contents, students will also learn to use the properties of functions to find approximate solutions to equations, experience the connection between functions and equations, and realize that function images are an intuitive tool for understanding and studying functions.

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In the definition domain, an independent variable x can only have one dependent variable y corresponding to it, and any y can find an x corresponding to it, of course, this x may not be unique, and the most important point of definition is that an x can only have a y

1.Functions are defined based on a set of numbers.

2.If the value of a function does not uniquely correspond to an independent variable, it is called a multi-valued function, and if it corresponds to a unique value, it is called a single-valued function.

In general, when we talk about functions, we mean single-valued functions.

3.Generally, the inverse function is studied in the case of a single-valued function, so it is required that the definition domain of the function must be one-to-one correspondence from the value domain to the value range, and the value range to the definition domain.

Traditional Definition:

In general, in a change process, if there are two variables x and y, if for any x there is a uniquely determined y corresponding to it, then x is said to be an independent variable and y is a function of x. The range of values of x is called the domain of the function, and the range of values of y is called the range of functions.

Modern definition. Let a and b be non-empty sets of numbers, and if, according to some definite correspondence f, there are uniquely definite numbers in set b for any number x in set a.

where x is called the independent variable, and if the definition domain is omitted, it generally refers to the set that makes the function meaningful.