(1) matching method: suitable for quadratic function types.

(2) Separation constant method: the numerator and denominator are unknown.

For example: y=(2x+ 1)/(x-3)

=[2(x-3)+7]/(x-3)

=2+7/(x-3)

Because 7/(x-3) is not equal to 0.

So y is not equal to 2.

(3) Inverse solution:

For example: y=(2x+ 1)/(x-3)

(y-2)x-3y- 1=0

So x=(3y+ 1)/(y-2)

So y is not equal to 2.

f(x)=(ax+b)/(cx+d)

F(x) is not equal to a/c.

(4) Discriminant method: use discriminant after inverse solution.

(5) Alternative methods

(6) Image method

Second, find the functional domain.

1, the function domain is the set of values of function independent variables, which is generally required to be expressed by sets or intervals; 2. The common question type is to use analytical expressions to find the domain. At this time, it is necessary to identify the independent variable, and then examine the position of the independent variable, which determines the scope of the independent variable. Finally, the problem of finding the domain boils down to the problem of solving the inequality group.

3. As mentioned above, the function definition domain in practical problems is not only limited by analytical expressions, but also by practical meanings, such as time variables generally taking non-negative numbers, and so on;

4. To solve the definition domain of the compound function y = f [g(x)], the value domain y=f(u, that is, the value domain of g(x) should be obtained from y = f (u) first, and then the value domain I1of x; Then the domain I2 of y = g(x) is found from g (x), and the intersection of I 1 and I2 is the domain of composite function.

5. The domain of piecewise function is the union of all intervals;

6. In order to solve the domain of the function with parameters, it is necessary to classify and discuss the parameters. If the definition fields of parameters are different in different ranges, they should be explained separately when stating the conclusion.

7. When finding the domain, it is sometimes necessary to classify the independent variables, but when describing the conclusion, it is necessary to find the union of each set obtained after classification as the domain of the function.

8. If the inverse function is used (that is, X is represented by Y), then the range becomes the domain, and then the value range obtained is the original domain.

For example, the value range of y=2x+ 1 is (2,6). Find the domain of x.

The inverse function is: x = y/2- 1/2, and the domain of y is (2,6).

Because this function is monotonically increasing, the value range is (1/2,5/2).

So the domain of the original title X is (1/2,5/2).

Of course, the example I gave is relatively simple, and it is difficult to estimate the general problem. The key point is to judge the monotonicity of the function.