I. Assemble

Definition and important properties of 1. subset: any set is its own subset, that is, AA. It is stipulated that an empty set is a subset of any set, that is, A. If AB and BA are involved, then A = B. If at least one element of AB and B is not in A, then A is called the proper subset of B, and it is recorded as AB. An empty set is the proper subset of any non-empty set. Set A has two subsets of n elements, 2- 1 nonempty subset and 2 nonempty proper subset.

2. Definition and important properties of complement set;

3. The essence of intersection and union: ANB=AAB, AUB=ABA.

4. Symbols of commonly used number sets: integer set z, natural number set n, positive integer set, rational number q and real number set r.

Second, the common problems of composite function

(1) Know that the domain of f(x) is A, and find the domain of F: In essence, if you know that the domain of g(x) is A, you can find the domain of X. ..

(2) Knowing that the domain of F is B, finding the domain of f(x): In essence, knowing that the domain of X is B, finding the domain of g(x).

(3) Knowing that the domain of F is C, finding the domain of F: In essence, knowing that the domain of X is C, so as to find the domain of g(x) first (that is, the domain of f(x)); Then take it as the range of h(x), and then find the range of x.

3. The function image has at most one common point with the vertical axis, but there may be no common point with the vertical axis.

4. Even functions symmetric about the origin are monotonous, but their monotonicity is just the opposite.

5. If odd function has monotonicity in the interval symmetrical about the origin, its monotonicity is exactly the same.