How to solve the analytic formula of the composite function?

The case of composite functions varies widely, and they are usually integrated as simple elementary functions. For example, (sinx) 2dx = 1-cos2x) 2]dx = dx 2-(1 2) cos2xdx =x 2-(sin2x 2) 2+c =x 2-sin2x 4+c can be integrated into an infinite series and then the generation will not get a simple elementary function.

The decomposition of the composite function can be decomposed layer by layer from the outer layer to the inner layer.

For example, y=sin 3x can be decomposed into y=u, u=sinv, and v=3x

Hello, there are a total of one of the methods:

1 Pending coefficient method: The pending coefficient method can be used when the analytic formula of the function is known.

2 Matching method: that is, it is known that f(mx+n)=....Match the following polynomial to the form mx+n, and finally replace it with x;

3 Commutation method: When the expression of the composite function f(g(x) is known, you can also use the commutation method to find the analytical expression of f(x). As with the matching method, it is necessary to pay attention to the change in the definition domain of the exchanged element.

4. Substitution method: When finding the symmetry function of a known function about a certain point or a straight line, the substitution method is generally used.

5. Constructing equations: If the known functional relationships are relatively abstract and simple, you can replace the variables, try to construct the equations, and obtain the analytic formula of the function by solving the equations.

6. Assignment method: When there are many variables given in the question and there are conditions such as "arbitrary", the variables with "arbitrariness" can often be assigned to make the problem concrete and simplified, so as to obtain the analytic formula.

7. Recursive method: If the conditions given in the question contain some kind of progressive relationship, you can recursively derive the series relation, and then obtain the analytical formula of the function by superposition, multiplication or iteration.

From f(x), when x<0, f(x)=x 2>0, so g(f(x))=x 2+2, x<0

When x>=0, f(x)=-x<=0, so g(f(x))=2-(-x)=2+x, x>=0I choose D

What ridge difference is the compound Qing stupid function Sakura?

In fact, it's very simple, a new function composed of two or multiple functions is a composite function, and the value range of the inner function is the definition domain of the outer function, and so on. For example, f(g(x)), the value domain of g(x) is the domain of the filial piety definition of the outer function f().

1, x x 2 2, f(x) f(x 2 2) 2(x 2) square .........

2，2f－x＋fx=2-3x

Combined with the original formula to eliminate f x, the mobile phone can be understood.