### Domain of definition and domain of value of a function

1, the domain of definition is “how x is chosen”, and the domain of value is “what x may be after the function is transformed”.

2, the value domain is determined by the domain of definition, but the domain of definition can not necessarily be inverted by the value domain. For example, f (x) = x, the definition and value domain are all real numbers, but the meaning is different, the definition of the domain x = R that “x can be any real number”, the value of the domain y = R that “x after the transformation of the function may be any real number”.

3. f(x)=x2, the definition domain is all real numbers, the value domain is all non-negative real numbers (0 and positive real numbers), this is because the square of a real number is necessarily 0 or a positive real number. f(x)=e^(1/x), the definition domain is all non-zero real numbers, the value domain is all the positive real numbers except 1.

### What are the three elements of the function in the first year of high school math: the definition of the domain, the value domain, the corresponding law refers to?

Solution: the definition of the domain: is the range of values of the independent variable x, the method of finding generally follow the following three principles: (1) when the number of the square to be opened to the even square, the number of the square to be opened ≥ 0; (2) the denominator ≠ 0, there are a few fractional lines, there are a few denominators ≠ 0; (3) in the application of the real situation, consider the real situation.

value range: is the range of values of the dependent variable y. Commonly used methods such as inverse function method, root formula method, image method, analytical method, etc., to be good at summarizing and categorizing. When you see a function, you have to think of what method to use.

y=f(x), the meaning of f is the law of calculation, meaning: the independent variable x through what kind of calculation process to get the value of the function y. Such as: y=f(x)=2x+4, the meaning of f is: x multiplied by 2, and then add 4, you get y. And: y=f(x)=2(x+2)

in the y=f(x)=2(x+2)

the meaning of f is: x plus 2, then multiplied by 2, you get y. And: y=f(x)=2(x+2)

the meaning of f is: x plus 2, then multiplied by 2, you get y. After that, multiply by 2 and you get y.

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

The domain of definition refers to the range of values of the independent variable; the domain of value refers to the range of values of the dependent variable.

An independent variable is a factor or condition that is actively manipulated by the researcher and that causes a change in the dependent variable; therefore, the independent variable is seen as the cause of the dependent variable. Dependent variable (dependentvariable), a specialized term in function, a functional relationship equation, some specific number will change with the change of another (or another several) will change the number of change, it is called the dependent variable.

For example, Y=f(X), which means that Y varies with X, Y is the dependent variable, and X is the independent variable.

Example:

The function y=x²+2The range of values of the independent variable of this function is the domain of real numbers i.e. R.

∴x can take any value and its domain of definition is R.

Again the minimum value of the function y when x ∈ R is 2, which is obtained at x=0.

∴The domain of the function is [2,+∞).

In the classical definition of function, the range of values of the dependent variable is called the range of values of this function, in the modern definition of function is the set of all the elements in the definition of the domain of all the elements of the corresponding law under a certain correspondence of all the elephants. That is, {y∣y=f(x),x∈D}

Common function value range:

y=kx+b (k≠0) has a value range of R.

y=k/x has a value range of (-∞,0)∪(0,+∞).

The domain of values of y=√x is x≥0.

y=ax^2+bx+c when a>0, the domain of values is [4ac-b^2/4a,+∞).

When a<0, the domain of values is (-∞, 4ac-b^2/4a].

The value domain of y=a^x is (0,+∞).