Who can tell me all the properties of parity of mathematical function. For example, odd + even =?

Who can tell me all the properties of parity of mathematical function. For example, odd + even =?

Odd ± odd = odd ± even = even odd x odd = even even x even = even odd x even = odd
Odd and even can't be judged
nature
1. Even function has no inverse function (even function is not monotone function in the domain of definition), and the inverse function of odd function is still odd function. 2. Even function has opposite monotonicity in two symmetric intervals about the origin in the domain of definition, 3. Odd ± odd = odd ± even = even odd x odd = even even even x even = even odd x even = odd (the domain of two functions should be symmetric about the origin). 4. For f (x) = f [g (x)]: if G (x) is an even function, then f [x] is an even function. If G (x) is an odd function and f (x) is an odd function, then f [x] is an even function, Then f (x) is an odd function. If G (x) is an odd function and f (x) is an even function, then f (x) is an even function. 5. The domain of definitions of odd and even functions must be symmetric about the origin