1. The undetermined coefficient method is generally used to find the analytical formula of known function types. The basic idea of undetermined coefficient method is to solve a mathematical problem with a certain form by introducing some undetermined coefficients and then transforming them into a problem of equations according to the conditions set by the problem.

2. Knowing the analytic formula of function f(x), find the analytic formula of compound function f[g(x)] and use method of substitution. That is to say, it is only necessary to replace x in the analytical formula of f(x) with g(x), which is simplified.

3. Given the expression of the compound function f[g(x)], method of substitution is generally used to find the analytical expression of f(x).

4. Given the analytic expression of a function in the local interval of the domain, the interval transfer method is generally used to find its analytic expression in the whole domain. That is, the problem on the interval of unknown analytical formula is transferred to the interval of known analytical formula for solution.

5. The relationship between f(x) and f( 1/x) is given (it can be regarded as a functional equation). If f(x) is needed, it needs to be eliminated (1/x). So we need to generate a new one about f(x) and f( 1/x) from the known relationship.

Function, a mathematical term.

Its definition is usually divided into traditional definition and modern definition. The essence of these two functional definitions is the same, but the starting point of narrative concept is different. The traditional definition is from the perspective of movement change, and the modern definition is from the perspective of set and mapping. The modern definition of a function is to give a set of numbers a, in which the elements are assumed to be X.

Apply the corresponding rule F to the element X in A, and record it as f(x) to get another number set B. Assuming that the element in B is Y, the equivalent relationship between Y and X can be expressed as y=f(x). The concept of function includes three elements: domain A, range B and corresponding rule F, among which the core is corresponding rule F, which is the essential feature of function relationship.

Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.