1, most even functions have no inverse function (because most even functions are non-monotonic in the whole definition domain), and a function and its inverse function are monotonic in the corresponding interval.

2. Even functions have opposite monotonicity in the two intervals symmetrical about Y axis in the definition domain, while odd function has the same monotonicity in the two intervals symmetrical about the origin in the definition domain.

3, odd odd = odd

Even number = even number

Odd x odd = even

Even x even = even

Odd x even = odd (the domains of two functions should be symmetrical about the origin).

4. For F(x)=f[g(x)]: If g(x) is an even function and F(x) is an even function, then F[x] is an even function.

If g(x) is odd function and f(x) is odd function, then F(x) is odd function.

If g(x) is odd function and f(x) is an even function, then F(x) is an even function.

5. The domains of odd and even functions must be symmetrical about the origin.