Advanced mathematics foundation_ Parity of functions

1. The parity of functions , It is a required test .

The premise of judging parity ：  The domain of a function must be symmetric about the origin .

Not all functions have parity ,  for example y = x³ + 1 ,  It is not symmetrical about the origin , It's not about y axial symmetry .

So the function Classified according to parity , Can be divided into

2. Next, let's look at an example

3. nature

stay f（x）,g（x） On the public domain of ：

Odd functions ± Odd functions = Odd functions

Even functions ± Even functions = Even functions

Odd functions × Odd functions = Even functions

Even functions × Even functions = Even functions

Odd functions × Even functions = Odd functions

The multiplication law of odd and even functions can be summarized as ： Identical even odd