Why does an odd function multiply even function to get an odd function?

Odd functions. Even Functions = Odd Functions Odd Functions Even=Odd FunctionsOdd Functions + Even FunctionsThe result is neither an odd function nor an even functionOdd Functions + Odd Functions = Odd Functions Odd Functions Odd Functions = Even Functions Odd Functions Odd Functions = Even Functions Even Functions Let Odd Functions be f(x) Even Functions as g(x) Use Odd Functions f(x)=-f(-x) Even Functions g(x)=g(-x) You can deduce it e.g. Odd Functions Even=Odd Functions f(x)*g(x)=f(x) then f(x)=- f(-x)*g(-x)=-f(-x) satisfies the form of the odd function.

The odd function multiplied by the even function equals the odd function. An even function multiplied by an even function is also equal to an even function, and an odd function multiplied by an odd function equals an even function. Parity of functions means that the values of the functions of the symmetry points about the origin are equal, which is the basic property of the functions, that is, their images have some kind of symmetry.

Addition rules for odd-even functions.

The odd function plus the odd function is the odd function.

The function obtained by adding an even function to an even function is an even function.

The function obtained by adding an even function to an odd function is a non-odd and non-even function.

Odd functions. The odd function refers to the fact that for any x in the definition domain of the function f(x) about the origin symmetry, there is f(-x)=-f(x), then the function f(x) is called an odd function.

Even functions. In general, if there is f(x)=f(-x) for any x in the domain where the function f(x) is defined, then the function f(x) is called an even function.

Odd functions. The odd function isEven functions.

The odd function multiplied by the odd function equals the even function. Odd function multiplication and even function are odd functions, odd function addition and subtraction of odd functions are odd functions, even function addition and subtraction of even functions are even functions, odd functions multiply odd functions are even functions, and even functions multiply even functions are even functions. An even function multiplied by an even function is an even function.

1. Addition rules for parity functions1) The odd function obtained by adding the odd function to the number of odd functions is the odd function.

2) The function obtained by adding the even function to the even function is the even function.

3) The function obtained by adding the odd function to the even function is a non-odd and non-even function.

2. Subtraction rules for odd-even functions1) The odd function is obtained by subtracting the odd function to obtain the odd function.

2) The even function is obtained by subtracting the even function.

3) The odd function minus the even function is a non-odd and non-even function.

3. Multiplication rules for odd-even functions1) The function obtained by multiplying the comma odd function by the odd function is an even function.

2) The odd function multiplied by the even function is the odd function.

3) The even function is multiplied by the even function to obtain the even function.

4. The division rules of odd and even functions1) The odd function divided by the odd function is an even function.

2) The odd function is divided by the even function to obtain the odd function.

3) The even function is obtained by dividing the even function.

It reads as follows:

1. Multiplying an odd function by an even function results in an odd function.

2. The result of an odd function plus an even function is neither an odd function nor an even function.

The proof is as follows: 1. Let f(x) be an odd function and g(x) be an even function:

Let t(x) = f(x)g(x).

It can be obtained from f(-x)=-f(x), g(-x)=g(x).

t(-x)=f(-x)g(-x)=-f(x)g(x)=-t(x) 。

t(x)=f(x)g(x) is an odd function.

2. Let f(x)=f(x)+g(x).

then f(-x)=f(-x)+g(-x)=-f(x)+g(x).

f(x)=f(x)+g(x) is neither odd nor even.

Formula: 1. If you know the function expression, for any x in the definition domain of the function f(x), it satisfies f(x)=f(-x) such as y=x*x; y=cos x。

2. If you know the image, the even function image is symmetrical with respect to the y-axis (straight line x=0).

3. The definition domain d of the even function is a necessary but not sufficient condition for the function to become an even function.

For example: f(x)=x 2, x r (f(x) is equal to the square of x, x is a real number), and f(x) is an even function.

Number. f(x)=x 2,x (-2,2](f(x) is equal to x squared, -2

Multiplying an even function by an odd function is an even function, and multiplying an even function by an even function is an even function.

Even Functions The result of an odd function is an odd function. Can be illustrated with definitions.

f(x) is an even function.

f(-x) = f(x) can be obtained

g(x) is an odd function.

g(-x) = g(x) can be obtained

h(x) =f(x).g(x)

h(-x)f(-x).g(-x)

f(x).g(x)

h(x) gives the h(x) odd function.

Even function multiply odd function = odd function.

Odd functions multiply and even functions are odd functions.

The addition and subtraction of odd functions is an odd function, the addition and subtraction of even functions is an even function, the multiplication of an odd function by an odd function is an even function, and the multiplication of an even function by an even function is an even function.

To determine the parity of the function, we must first look at the defined domain, if the defined domain is symmetrical about the origin, then discuss the parity, otherwise it is directly determined to be a non-odd and non-even function.

Continuity of Functions:

In mathematics, continuity is a property of a function. Intuitively, a continuous function is one in which when the change in the input value is small enough, the change in the output is also small enough.

If some small change in the input value produces an abrupt jump in the output value that cannot even be defined, the function is said to be discontinuous (or discontinuous).

Without the concept of limits, the following method can be used to define the continuity of a real value function.

Still consider the function. Suppose C is an element in the defined domain of F.

A real function is a function that defines a field in which both the domain and the range of values are real numbers. One of its characteristics is that it is generally possible to draw a figure on coordinates.

Virtual functions are an important concept in object-oriented programming. When inheriting from a parent class, the virtual function and the inherited function have the same signature.

However, during the runtime, the runtime system will automatically select the appropriate specific implementation to run according to the type of object. Virtual functions are the basic means of implementing polymorphism in object-oriented programming.

Odd functions. Even functions must be odd functions.

Even if there is a special case f(x) =x, g(x) =0 then f(x) is an odd function and g(x) is an even function and is also an odd function. f(x)g(x) =0 is an even function and is also an odd function.

The above conclusion remains correct.

It must be an odd function, oh dear.

There are odd functions f(x) and odd functions g(x).

But Sun Fan hail sedan chair feast: f(x)=-f(-x) g(x)=-g(-x)h(x)=f(x)*g(x).

h(-x)=f(-x)*g(-x)=-f(x)*-g(x)=h(x)So h(-x)=h(x).

h(x) is an even function, then the sail.