It is so difficult to define the domain of the function in the first year of high school, and it is

Let me show you a question I answered earlier.

If the domain of the function f(x) is [0,1], then what is the domain of the function f(2x) f(x)?

The domain of the function f(x) is defined as [0,1] (in the range of x under the rule of f).

i.e. the bracketed range is [0,1],0 2x 1 .0≤x≤1/2

0≤x+2/3≤1...2/3≤x≤1/3

0≤x≤1/3

Define the domain as [0,1 3] (define the range where the domain is x).

Ask. Uh, that's the step 0 x+2 3 1....2/3≤x≤1/3

0 x 1 3 I don't understand, can you be more detailed?

f(2x), f(x+2 3) are actually no longer f(x) functions, but the rules are the same.

But when m=2x, n=x+2 3, f(m),f(n) is the same as f(x), where m,n,x are independent variables, and the definition domain refers to the range of independent variables under f's rule, and m,n ranges are the same [0,1].

And then back to the functions f(2x), f(x+2 3), the argument is x

If you want to define a domain, you need to have a range of x, and you are taking the intersection of the two.

Ask. I'm sorry, I'm a little stupid, or I don't understand, can you be more detailed?

f(2x), f(x+2 3) are actually no longer f(x) functions, but the rules are the same.

But when m=2x, n=x+2 3, f(m),f(n) is the same as f(x), where m,n,x are independent variables, and the definition domain refers to the range of independent variables under f's rule, and m,n ranges are the same [0,1].

And then back to the functions f(2x), f(x+2 3), the argument is x

If you want to define a domain, you need to have a range of x, and you are taking the intersection of the two.

Which of these steps you don't understand, why don't you understand, talk about it.

Ask. If you want to define a domain, you need the scope of x, and this is the step when you take the intersection of the two.

And the definition domain refers to the range of independent variables under the f rule, as I said in this step, in f(2x), f(x+2 3), the independent variable is x

Scope of requirement x.

And let f(x) = f(2x) + f(x+2 3).

Under the f rule, x should satisfy f(2x), f(x+2 3), if not, then this formula is meaningless, so the x range in the two functions is required, and it must be satisfied at the same time, so take the intersection.

Teach you a method, when encountering a fraction, you have to consider that the denominator is not zero, and the formula containing the root number takes into account that the root number is greater than zero...

1.The definition domain of the function refers to the input value, that is, the range of x in 2x-1, so it is 0 x 1, so the parentheses in -1 2x-1 1 refer to the closed interval, that is, there is equal to and the small parenthesis on the right is the open interval, so it is less than The range of objects applied by the same correspondence rule is the same, so the range of 2x-1 and 1-3x is the same, so -1 1-3x 1 solves the value of x to be 0 x 2 3

2.Think of it this way: the status of x in parentheses is the same as the status of 2x+1, and the required definition domain is the range of x in 2x+1.

3.This problem is the same as the first one, [-2,3] is the range of x, not the range of x+1, so we need to find the range of x+1 first, because x+1 and 2x-1 are the same correspondence rule, so they are the same range, so -1 2x-1 4 can then find the definition domain.

All the same, as long as you know that the domain of f(2x-1) is [0,1), which refers to the range of x in 2x-1, x first becomes t=2x-1, and then substituted into f(t), f(2x-1) defines the domain of [0,1) so 0 x<1 so -1 t=2x-1<1, so f(t) defines the domain.

1, because f(2x-1) defines the domain as [0,1) so 0 x<1 so 0<=2x<2 -1 2x-1<1

2, The domain of the function f(x) is [-1,4], i.e. -1 x 4 so -1 2x+1 4 so -1 x 3 2

3, the domain of the function f(x+1) is [-2,3], i.e. -2 x 3, so -1 x+1 4, so -1, 2x-1, 4, so 0 x

P.S. The defined domain in the known condition is the restriction of x, and the range of the whole parenthesis is found according to the known condition, and then the range of x in the parentheses is the defined domain of the requirement.

x refers to the domain in which f(x) is generated, and the x in "2x-1" f(x).

a<=x<=b

a<=-x<=b Find the intersection and you can get the first thing out of the Zhengyan Pay attention to the jujube pure condition-b2: Replace the m-1 algebra to get f(m-1)=f(m)+2 Do it yourself Try it yourself.

A f(x) is defined by the quiet domain (a,b), then for f(-x),a3c-x3cb, i.e., the domain of its meditation permeability x belongs to the domain of (-b,a), and finally, the domain of f(x) is their union (-b,b).

(1) 1-tanx is the denominator, so 1-tanx cannot be equal to 0, i.e. tanx is not equal to 1

So x is not equal to k + 4

2) 1+2sinx is also the denominator and cannot be equal to 0, so sinx is not equal to -1 2

So x is not equal to - 3+2k

3) Because there is no constraint, x can take r (all real numbers) (4) because the book in the root number should be greater than or equal to 0

So cosx 2 should be less than or equal to 1

Whereas, the maximum value of cosx 2 is 1

So x still takes r

In short, defining the domain is to find the constraints of x in the equation.

Finding the meaningful x value range of the function expression.

Method: List the groups of inequalities according to the following criteria: 1 The denominator is not zero 2 The expression under the root number is not negative 3 The periodicity of the function 4 The range of values of special functions, such as the range of values of the inverse function of trigonometric functions is limited, arcsinf(x), then -1<=f(x)<=1, etc.

Then solve the group of inequalities and find the common solution.

1.Definition. In a functional relationship, the range of values of the independent variable is called the domain of the function.

2.Classify. The definition domain of a function is defined according to the problem that the function is trying to solve, and there are generally three ways to define the domain of a function:

1) Naturally defined domain, if the correspondence of the function is represented by an analytic expression, the range of values of the independent variable that makes the analytic meaningful is called the natural definition domain. For example, a function, for the analytic expression of the function to be meaningful, then, hence the natural domain of the function;

2) The function has a practical background for specific applications. For example, a function represents the relationship between velocity and time, and in order for a physical problem to be meaningful, time, and therefore the domain of the definition of the function;

3) Artificially defined defined domains. For example, when studying a function, only a functional relationship in the range of [0,10] is examined for the independent variables of the function, so the definition domain of the function is [0,10].

3.Defining the domain of the function: A function formed by several basic functions through four operations, and the domain is defined as the common part that makes each part meaningful.

Principles: (1) The denominator of a fraction cannot be zero; (2) The inside of the even square root must be non-negative, that is, greater than or equal to zero; (3) The true number of logarithms is positive, and the base number of logarithms is greater than zero and not equal to 1.

According to the above principle, the definition domain can be found by listing inequalities or groups of inequalities.

The value range may be difficult.

What's so hard about defining a domain?

First of all, it is certain that a is not equal to 0 and that a is greater than 0In order to satisfy the definition domain r, only the discriminant formula t=36m 2-4a (m+8) is less than or equal to 0 and a is greater than 0

Using the principal element change method, a one-time function f(a)=-4a(m+8)+36m 2 is constructed with respect to the independent variable a

a is greater than 0) so only f(0)=36m2 is less than or equal to 0, i.e. m=0,