If any x in the definition domain of the function f(x) has f (-x) = f(x), the function f(x) is called an even function. If any x in the domain of function f(x) has f (-x) =-f(x), then function f(x) is called odd function. When judging the parity of a function, we should first look at whether its domain is symmetrical about the origin. A function is a odd function or even function, and its domain must be symmetrical about the origin. In addition, the monotonicity of even-numbered functions in symmetric interval is opposite, and the monotonicity of odd-numbered functions in the whole domain is consistent.

The method of judging the parity of function

1, first decompose the function into common general functions, such as polynomial x n, trigonometric function, and judge parity.

2. According to the algorithm between decomposition functions, there are generally only three kinds: f(x)g(x), f(x)+g(x) and f(g(x)) (division or subtraction can be transformed into corresponding multiplication and addition).

3. If one of f(x) and g(x) is odd function and the other is an even function, then f(x)g(x) is odd function, f(x)+g(x) is neither odd function nor even function, and f(g(x)) is odd function.

4. If f(x) and g(x) are even functions, then f(x)g(x) is even, f(x)+g(x) is even, and f(g(x)) is even.

5. If both f(x) and g(x) are odd function, then f(x)g(x) is even, f(x)+g(x) is odd, and f(g(x)) is odd.