- Chinese name
- Define Fields
- Foreign name
- domain of definition
- Applicable fields
- function
- Interpretation
- One of the three elements of a function
- Type
- Mathematical, physical and chemical terms
Definition 1: Let x and y be two variables, and the variation range of variable x is D. If for each number x ∈ D, variable y always has a certain value corresponding to it according to a certain rule, then y is called x function , recorded as y=f (x), x ∈ D, x is called the independent variable, y is called the dependent variable, and number set D is called the domain of this function. [1] Definition 2: A. B is two Nonempty number set , from aggregate A to set B mapping , called a function from set A to set B. record as or Where A is called Define Fields 。 Usually, use letter D means. Generally, the definition field is the value range of x in F (X). 1. Given domain: for example: function The domain of is the given aggregate {1,2}。 2. Definition domain of general function: all real numbers that make the function meaningful. For example, the definition field of function y=1/x is 。 R is any real number. It can also be written as 3. Practical problem: seek the definition domain according to the specific situation.
4. Of course, it will also be used in dynamic physics to find variables
abstract Function definition field There are three common types of questions: Known The definition field of Definition field of Example 1 Known The definition field of is (- 1, 1) Definition field of ∴ The domain of is (0, 1) Known The definition field of Definition field of Example 2 Known The definition field of is (0, 1) Definition field of Solution: known 0
∴-1<2x-1<1
∴ The definition field of is (- 1, 1) Pay attention to comparing Example 1 and Example 2 to deepen understanding Defined as x Value range Meaning of. Known Find the domain of f (h (x)) Example 3 Known The definition field of is (0, 1) The domain of the. Slightly solve: as example 2, first calculate The definition field of is (- 1, 1), and then as shown in Example 1 ∴ The domain of is (0, 2) It refers to the collection of all real numbers that make a function meaningful.
It is mainly based on:
① fraction The denominator of cannot be zero ② Even degree root Of Number of prescriptions Not less than zero ③ Logarithmic function The true number of must be greater than zero ④ exponential function And logarithmic base number Must be greater than zero and not equal to 1 Example 4 Known , seek Of Define Fields 。 Note: The answer is usually section express. Example 5 Known , seek The domain of the. ∴ The definition field of is (- 1, 2) The definition field of function in function word problems should be based on the actual situation solve 。 Example 6 Statistics of a factory show that the defective product rate p and the daily output x (pieces)（ ）The relationship between x | one | two | three | four | … | eighty-nine |
p | 2/99 | 1/49 | 2/97 | 1/48 | … | 2/11 |
We also know that the profit is 100 yuan for each genuine product and the loss is 100 yuan for each defective product
Ask the factory for the day Profit T (yuan) About day Function of output x (piece); Solution: Why? When the output of the day is x pieces, the defective rate The number of defective products is: ， quality goods Number: therefore 
