How do I solve a composite function? How do you solve a composite function?

Composite functions are important in commutation.

You can convert it to a simple function.

Swapping is to replace an unknown number.

A formula with another unknown.

A hierarchical solution, expressed as an unknown quantity, by an equation. And so on.

Composite functions require us to master their theoretical knowledge and theorems as well as skills. You have to "eat" the textbook, and then you have to find extracurricular questions to practice, and by the way, you have to master other ways to solve them. You can use many ways to change dollars, special numbers "1", etc.

I can answer the specific questions for you.

The ultimate goal is to simplify complex multi-multiple functions.

y=log(2)(x^2+3x+2)

2 is the bottom. For example.

Finding its increasing interval?

First, let's look at (x 2+3x+2) as t

y=log(2)t

Let's start with the nature of logs.

When the base is less than 1, it decreases as t increases.

When the base is greater than 1, it increases with the increase of t.

We also need to consider that t should be greater than 0, so that we can start to ask for it.

y=log(2)t is incremental, i.e., it increases as t increases.

t=(x 2+3x+2), the problem wants the increasing interval of y, so t is required to be larger and larger, first (x 2+3x+2)> 0,x>-1,x<-2

t=x 2+3x+2=(x+3 2) 2-1 4, we can see that the increment of t is (-3 2, +infinity).

Combined with the definition domain (x>-1, x<-2).

Answer. for (-1, +infinity).

A hierarchical solution, expressed as an unknown quantity, by an equation. And so on.

The ultimate goal is to simplify complex multi-multiple functions.

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.

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>=0Choose D

The definition lets y=f( )= (x), when x changes in the definition domain d of = (x), the value of = (x) changes in the definition domain df of y=f( ), so that the variable x and y form a functional relationship through the variable, denoted as.

y=f( )=f[ (x)] is called a composite function, where x is called the independent variable and is the intermediate variable, and y is the dependent variable (i.e., the function).

This paragraph] generates conditions.

Not any two functions can be compounded into a composite function, only if the intersection of the domain z of = (x) and the definition domain df of y=f( ) is not an empty set.

If the domain of the function y=f(u) is b, and the domain of the function u=g(x) is a, then the domain of the composite function y=f[g(x)] is.

d = [this paragraph].

If the minimum positive period of y=f(x) is t1, and the minimum positive period of = (x) is t2, then the minimum positive period of y=f( ) is t1*t2, and any period can be expressed as k*t1*t2 (k belongs to r+).

In this paragraph, the increase or decrease is determined by the increase or decrease of y=f(x), = (x). That is, "increase and increase, decrease and decrease, increase and decrease", which can be simplified to "increase and decrease with difference".

The steps to determine the monotonicity of a composite function are as follows: (1) Find the domain of the composite function definition;(2) Decompose the composite function into several.

common functions (primary, quadratic, power, finger, pair);(3) judging the monotonicity of each common function;(4) Place the middle.

The value range of the variable is converted into the value range of the independent variable(5) Find the monotonicity of the composite function.

For example, discuss the monotonicity of the function y=.

Solution: The function defines the domain as r.

Let u=x2-4x+3,y=.

The exponential function y=is a subtraction function on (-), u=x2-4x+3 is a subtraction function on (- 2], an increasing function on [2,+, function y=an increasing function on (- 2], and a subtraction function on [2,+.

The composite function is used to find the range of parameter values.

Finding the range of values of a parameter is an important problem, and the key to solving the problem is to establish an inequality group about this parameter.

Transform all known conditions.

What ridge difference is the compound Qing stupid function Sakura?

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().

。。What do you want to solve?。。 Generally, it is necessary to set up an intermediary amount, such as u, t, etc.

First read the question, call out the composite part, replace this part with x or y, write the function with x as the independent variable and the function of the composite part with x as the dependent variable, solve them separately, and finally bring in the answer.

You might as well put a question up.

Helped you out.

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