I. Settings and functions

Content intersection and complement set, and power exponential pair function. Parity and increase and decrease are the most obvious observation images. When the compound function appears, the law of property multiplication is distinguished. To prove it in detail, we must grasp the definition. Exponential function and logarithmic function are reciprocal functions. Cardinality is not a positive number of 1, and 1 increases or decreases on both sides. The domain of the function is easy to find. Denominator cannot be equal to 0, even roots must be non-negative, and zero and negative numbers have no logarithm. The tangent function angle is not straight, and the cotangent function angle is uneven; The real number sets of other functions have intersection in many cases.

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.