Generally speaking, let the range of function y=f(x)(x∈A) be C. If there is function g(y) everywhere, such 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 (- 1) (x) are the definition domain and value domain of the function y=f(x) respectively. The most representative inverse functions are logarithmic function and exponential function.

Generally speaking, if X and Y correspond to a corresponding relation f(x) and y=f(x), then the inverse function of y=f(x) is 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.

For example, the inverse of a function is.

Composite function of extended data inverse function

This content belongs to advanced mathematics. What is the simplest and most basic function among functions? Needless to say, it must be our identity function y=x, which is the same as 1 in our number, so we write the identity function as "1x".

The basic operation of numbers is addition, subtraction, multiplication and division, and functions also have operations. Although there are addition, subtraction, multiplication and division, what belongs to the function itself is the compound and inverse function. We know that in real numbers, the product of x and 1/x is equal to 1, and the compound operation of functions has similar properties. The composition of functions f and g is denoted as f○g, so the following properties hold: f-1f =1x; 1x f = f .

The first formula explains many problems. In fact, these are all contents of advanced algebra. In every closed system, there is a "unit 1", which has its own algorithm. The function is 1x, the real number is the number 1 and so on.

References:

Baidu encyclopedia-inverse function