Take y = 1+e x as an example:

Find the range of the function first, 1

Convert the function into a function whose x is y: y-y-1= e x, x = ln(y- 1).

Replace x with y, and get the inverse function y = ln(x- 1) with x, and its domain is 1

Extended data:

Properties of inverse function:

The necessary and sufficient condition for the existence of the inverse function of (1) function is that the domain and value domain of the function are mapped one by one;

(2) The function and its inverse function are monotone in the corresponding interval;

(3) Most even functions have no inverse function (when the function y=f(x), the domain is {0}, and f(x)=C (where c is a constant), then the function f(x) is even and has an inverse function, and the domain of the inverse function is {C} and the range is {0}). Odd function doesn't necessarily have an inverse function. When it is cut by a straight line perpendicular to the Y axis, it can pass through two or more points, that is, there is no inverse function. If a odd function has an inverse function, its inverse function is also odd function.

(4) The monotonicity of continuous functions is consistent in the corresponding interval;

(5) The strict increase (decrease) function must have the inverse function of strict increase (decrease);

(6) Inverse functions are unique to each other.