1. Conventional notation for inverse functions

　　Traditionally, people always use to represent the independent variable and to represent the dependent variable. Therefore, the inverse function of the function is often rewritten as

( or ).

　　According to the concept of function , the essence of a function is the correspondence between variables. As long as the correspondence remains unchanged, it does not matter what letters are used to represent the independent variables and dependent variables. The symbol representing the correspondence between and has not changed. They are the same function, that is, is also the inverse function of .

　　For example, the inverse function of on the interval is written as .

　　2. How to find the inverse function

　　If the given function is single-valued and monotonic in its domain , then is regarded as the independent variable and is regarded as the dependent variable, and the solution is

or ,

According to custom, it is recorded as  or  , which is the inverse function of the function  ; the inverse function of the piecewise function should be found piecewise, and its general method can be expressed as

.

　　3. Symmetry of the graph of a function and its inverse function

　　In the same rectangular coordinate plane , the graph of the direct function and its inverse function is symmetrical about the straight line ( see the figure below ) .

　　Because if is a point on the graph of , then is . vice versa. And and are symmetrical about the straight line , that is, the perpendicular bisector segment of the straight line .

[ Animation ]