Monotonicity of monotone increasing function is increasing.
Monotonicity of monotone decreasing plus monotone decreasing function is decreasing.
Monotonicity of monotone increasing and decreasing functions is increasing.
Monotonicity of monotone decreasing and monotone increasing functions is decreasing.
Multiplication and division are uncertain.
Compound function:
1. The monotonicity of the inner and outer layers increases.
2. The monotonicity difference between the inner layer and the outer layer is reduced.
As the saying goes: the same increase is different.
References:
About parity:
1. The sum (difference) of two odd function is still odd function, and the sum (difference) of two even functions is still even.
2. The product sum quotient of two functions with the same parity (denominator is not 0) is an even function, and the product sum quotient of two functions with opposite parity (denominator is not 0) is a odd function.
On monotonicity:
1. Functions f(x) and f(x)+c(c is a constant) have the same monotonicity.
2.c>0, functions f(x) and c*f(x) have the same monotonicity; C<0, functions f(x) and c*f(x) have opposite monotonicity.
3. If the functions f (x) and g (x) are both increasing (decreasing) functions, then f(x)+g(x) is still an increasing (decreasing) function.
4. if f (x) >; 0, g(x)>0, f(x) and g(x) are all increasing (decreasing) functions. Then f(x)*g(x) is also an increase (decrease) function; If f (x)