First, the essence of function. Personally speaking, it is the process that A can be processed into finished product B through some machine action (a set of rules) by giving a judgment that meets the processing conditions (definition domain). A and b are independent variables and function values, respectively. A raw material can only be processed into a product, which is the limiting condition of the mapping law.

On this basis, the rest is easy to understand. Y=f(x) y=g(x) is the same. F and G are just different mapping rules representing different processing methods.

Inverse function: inverse mapping, the inverse process of law, (a, b)-> (b, a), which is the essence.

Image transformation: the transformation of f(x) is around x, such as the bisection of f(x- 1) right 1 and the f(2x)x axis, which must be memorized regularly.

Monotonicity: first strictly grasp the definition, especially the proof. Remember that common functions are monotonous: power refers to quadratic (symmetry axis is the key) hyperbola y = x+a \ x

Power refers to the skill of doing more calculation problems.

PS: Don't forget the definition domain for all function problems.