Parity function operation:

The sum obtained by adding two even functions is even function, the sum obtained by adding two odd function is odd function, the sum obtained by adding an even function and a odd function is non-odd function, the product obtained by multiplying two even functions is even function, the product obtained by multiplying two odd function is even function, and the product obtained by multiplying an even function and a odd function is odd function.

Definition of function:

If any x in the function definition domain has f (-x) =-f(x), the function f(x) is called odd function. If any x in the function definition domain has f(-x)=f(x), the function f(x) is called an even function.

If f(-x)=-f(x) and f(-x)=f(x) are true for any x in the function definition domain, then the function f(x) is both a odd function and an even function, which is called a parity function. If neither f(-x)=-f(x) nor f(-x)=f(x) can be established for any x in the function definition domain, then the function F (x) is neither a odd function nor an even function, which is called a parity function.

As one of the most important properties of high school mathematics function, function parity has strong regularity, and its form of college entrance examination questions is flexible and changeable. We can examine the judgment of function parity independently, and use parity to find parameters and analytical expressions. It can also be integrated with monotonicity, periodicity, symmetry, function image and inequality of functions to make some comprehensive contents.

The way to examine the parity of a function in multiple-choice questions is to give an analytical expression of a complex variable function, and then according to the analytical function, consider the parity, monotonicity, special point and range of the function comprehensively to judge which of the four options of ABCD is its approximate image.

Sometimes multiple-choice questions and fill-in-the-blank questions will also give an analytical expression of an odd (even) function in a sub-interval of the definition domain, and then find the analytical expression of its symmetric interval. Let's introduce the related knowledge of function parity in detail.

Function parity refers to the symmetry of the function itself. If the image of the function itself is symmetrical about the origin (that is, taking the origin as its symmetry center), then the function is called odd function; If the image of a function is symmetrical about the Y axis (that is, taking the Y axis as the symmetry axis of its image), the function is called an even function. Let's introduce the related knowledge of function parity in detail.