Even function+even function = even function

Odd Function * Odd Function = Even Function

Even Function * Even Function = Even Function

Odd Function * Even Function = Odd Function

Parity of compound function: even if it is internal, it is odd if it is external;

Monotonicity of compound function: mutual increase and mutual decrease.

Extended data:

Prove by definition

1, odd function plus odd function equals odd function.

Let f(x) and g(x) be odd function, and h(x)=f(x)+g(x).

Then h (-x) = f (-x)+g (-x) =-f (x)-g (x) =-(f (x)+g (x)) =-h (x).

So h(x) is odd function.

2. Even function plus even function equals even function.

Let f(x) and g(x) be even functions, and h(x)=f(x)+g(x).

Then h (-x) = f (-x)+g (-x) = f (x)+g (x) = h (x).

So h(x) is an even function.

3. odd function addition function is equal to nonsingular non-even function.

Let f(x) be odd function, g(x) be even function, and h(x)=f(x)+g(x).

Then h(-x)=f(-x)+g(-x)=-f(x)+g(x)

Obviously, h(-x) is not equal to h(x), nor is it equal to -h(x).

Therefore, h(x) is a parity function.

4. Constant terms are regarded as even functions.

Let f(x)=k(k is a constant)

f(-x)=k=f(x)

So f(x) is an even function.