1. Solving x from the original function formula is represented by y. ..

2. exchange x and y.

3. Point out the domain of the inverse function.

Generally speaking, let the range of function y=f(x)(x∈A) be C. If a function g(y) is found to be equal to x everywhere, such a function x = g(y) (y ∈ c) is called function y = f (x) (x ∈). The definition domain and value domain of the inverse function y = f-(x) are the definition domain and value domain of the function y = f-(x) respectively.

Generally speaking, if X and Y correspond to a certain correspondence f(x) and y=f(x), is the inverse function of y=f(x) x=f(y) or y=f? ㈩. The condition for the existence of the inverse function (single-valued function by default) is that the original function must be in one-to-one correspondence (not necessarily in the whole number domain). Note: superscript "? 1 "does not represent a power.

Existence theorem of inverse function: a strictly monotone function must have a strictly monotone inverse function, and the monotonicity of the two functions is the same.

Properties of inverse function:

The (1) function f(x) and its inverse function image are linearly symmetric about y = x.

(2) The necessary and sufficient condition for a function to have an inverse function is that the domain of the function is mapped to the domain of the function.

(3) The function and its inverse function are monotonic in the corresponding interval.