Generally speaking, if it is determined that F corresponding to the function y=f(x) is a one-to-one correspondence from the definition domain to the value domain of the function, then the function determined by the inverse of f- 1 is called the inverse function of the function, and the definition domain and value domain of the inverse function x=f- 1(x) are the function y=f(x, for example. Solve x from the original function equation, that is, use y to represent x 2, use y to replace all x, and use x to replace all y, and get the properties of the reaction function in the inverse function: (generally, it is an explicit function) (1) Two images of functions that are inverse functions. (2) The necessary and sufficient condition for a function to have an inverse function is that the function is monotonic in its domain; (3) A function and its inverse function are monotonic in the corresponding interval; (4) Even functions do not necessarily have inverse functions, and odd functions do not necessarily have inverse functions. If a odd function has an inverse function, its inverse function is also odd function. Universities are divided into explicit functions and implicit functions, and the inverse function of explicit functions has all the above properties. Properties of implicit functions: (1) All implicit functions have inverse functions; (2) Two mutually inverse images are symmetrical about the straight line y = x; (3) The monotonicity of continuous functions is consistent in the corresponding interval.