① Matching method: transform it into a quadratic function and evaluate it by using the characteristics of the quadratic function; Often converted into:;

(2) Inverse solution: the value range obtained by inverse solution is expressed by and then obtained by solving inequality; Commonly used to solve, such as:

(4) Substitution method: transforming variables into functions of assignable fields and returning to ideas;

⑤ Triangular Bounded Method: Transform it into a function containing only sine and cosine, and use the boundedness of trigonometric function to find the domain;

⑥ Basic inequality methods: transformation and modeling, such as: using the average inequality formula to find the domain;

⑦ Monotonicity method: The function is monotonous, and the domain can be evaluated according to the monotonicity of the function.

⑧ Number-shape combination: According to the geometric figure of the function, the domain is found by the method of number-shape combination.

1. derivative method

It is the most routine and difficult to find the extremum and extremum point of monotonicity by derivative, but the calculation is often complicated.

2. Separation constant

For example, x 2/(x 2+ 1) divides it into1-1(x 2+1) and then judges the range.

3. The numerator and denominator are divided by a variable.

For example, if x/(x 2+1) is divided by x at the same time, the range of the denominator of 1/(x+ 1/X) can be easily found, and then it can be brought into the whole function.

4. Alternative methods

It can be said that it is an expansion of 3.

For example, (x+1)/(x 2+1), it is impossible to judge if the denominator is divided by x at the same time.

Let t = x+ 1, then express x 2 as (t- 1) 2, and then divide the numerator and denominator by t at the same time, which becomes the situation in 3.

5. Basic alternative methods

The type is1(x+1)+1/(x+1) 2, etc. , directly make t = 1/(x+ 1), find out the domain of t, and you can quickly convert the function into such as. Of course, pay attention to the domain of t.

6. Reciprocity method

And 2 are basically the same. For example, x/(x 2+1) first finds its reciprocal x+ 1/x, and then back, 2 and 6 are basically the same.

The above are some basic common methods, of course, we should pay attention to comprehensive application.