The Solution of Mathematical Resolution Function of College Entrance Examination and Its Common Knowledge Points (1)
Common solutions to analytic functions;
(1) undetermined coefficient method: (known function types, such as linear function, quadratic function, inverse proportional function, etc. ): If the structure of f(x) is known, you can set an expression with parameters, and then list the equations or equations according to the known conditions, so as to find the undetermined parameters and get the expression of f(x). The undetermined coefficient method is an important mathematical method, which is only suitable for solving the analytical formula of known functions.
(2) Substitution method (pay attention to the range of Singapore dollar): We know the expression of f(g(x)). If we ask for f(x), we always represent t=g(x), then we can get it.
, and then substitute into the expression of f(g(x)), so as to get the expression of f(t), that is, the expression of f(x).
(3) Matching method (whole replacement method): If the expression of f(g(x)) is known, it is difficult to find the expression of f(x) by replacement method (for example, g(x) has no inverse function). You can regard g(x) as a whole, replace the right side with a formula composed of g(x), and then substitute it to get f(x).
(4) Elimination method (e.g. the independent variables are reciprocal, f(x) is known as odd function, and g(x) is an even function, etc. ): If the form of an equation with a function as an element is known, if you can try to construct another equation to form an equation group, and then solve this equation group to find the function element, this method is called elimination method.
(5) Assignment method (special value substitution method): When finding the expressions of some functions or finding some function values, sometimes some variables in known conditions are assigned to make the problem simple and clear, so it is easy to find the expressions of functions.
Solution of Mathematical Resolution Function in College Entrance Examination and Its Common Knowledge Points (Ⅱ)
Finding resolution function is an important content of middle school mathematics and one of the important test sites of college entrance examination. In this paper, the basic method of solving the resolution function is given for teachers and students' reference.
First, the definition method
The method of finding its analytic expression according to the definition of function.
Example 1. known
, beg
.
Solution: Because
Second, alternative methods.
known
T as a whole, exchange elements and find out
The method.
Example 2. The same example is 1.
Solution: Order
, so
, so
. Commentary: Do we have to consider the method of substitution to find the resolution function? Yuan? The value range of, that is
The field of.
Third, the equation method
According to the meaning of the question, the method of solving analytic function by equation is established.
Example 3. Known functions defined on r
satisfy
, beg
Analytical formula of. Solution:
, ①
②
get
, so
.
Comments: The key to solving analytical formula by equation group method is to construct another equation according to the characteristics of formulas in known equations.
Fourth, professional methods.
The method of finding the resolution function by taking the special value of a variable.
Example 4. Known function
The domain of is r, which exists for all real numbers x and y.
, beg
Analytical formula of. Solution: Order
order
, so
, so
Verb (verb abbreviation) undetermined coefficient method
Given the type of resolution function, we can set the form of its analytical formula, and establish the equation of undetermined coefficient according to the known conditions, so as to find out the method of resolution function.
Example 5. Known quadratic function
The quadratic coefficient of is a, and the inequality
The solution set of is (1, 3), and the equation
There are two equal real roots. Find it.
Analytical formula of. Solution: Because
The solution set is (1, 3), let.
, so
① Through the equation
get
②
Because equation (2) has two equal real roots,
therefore
, namely
solve
and
, will.
( 1)
Click next to share more? The Solution of Mathematical Resolution Function of College Entrance Examination and the Induction of Common Methods and Knowledge Points