(1) definition method

It is the main method to judge the parity of a function by definition. First find the definition domain of the function and observe whether it is symmetrical about the origin. Secondly, simplify the function, then calculate f(-x), and finally determine the parity of f(x) according to the relationship between f(-x) and f(x).

(2) Have the necessary conditions.

The domain of a function with parity must be symmetrical about the origin, which is a necessary condition for the function to have parity.

For example, the domain of the function y= (-∞, 1)∩( 1,+∞) is asymmetric with respect to the origin, so this function does not have parity.

(3) Using symmetry

If the image of f(x) is symmetrical about the origin, then f(x) is odd function.

If the image of f(x) is symmetric about y, then f(x) is an even function.

(4) Operating with functions

If f(x) and g(x) are odd function defined on D, then on D, f(x)+g(x) is odd function, and f(x)? G(x) is an even function. Simply put, it is "odd+odd = odd, odd × odd = even".

Similarly, "even even = even, even × even = even, odd × even = odd".