Inverse And Composition Of Function

In mathematics the Inverse Function is considered as a function that undoes another function. If ‘g’ is a called a function then the inverse of the function ‘g’ is denoted as g^-1.
The theorem for composition of inverse Functions is stated as follows-
Suppose that there are two Functions named ‘f’ and ‘g’, this would be invertible functions such that the compositions of these functions f o g will be well defined. Mathematically this can be written as shown below-
(f o g)^-1 = g^-1 o f^-1,
To have a better understanding about the composite and inverse functions the following would be helpful.
The function composition always works from right to the left in mathematics. Here (f o g)^-1 is the reverse of the process (f o g), this can be understood better by considering the functions in a different way.
Consider the function ‘g’ as putting that function on one's socks, then putting that on one's shoes. As the reverse process of (f o g) is the (f o g)^-1 which is taking off one's shoes (that is f^-1) and followed by taking off one's socks which is the function g^-1.
To find inverse of a function there are a number of ways in mathematics and mostly the inverse of a function is preferred with the help of graphs and the algebraic operations. In other words inverse functions re defined as:
“For each Ordered Pair (x, y) in a function the denotation be ‘g’, there would be an another ordered pair (y, x) definitely in the inverse function.”
The composition of a function can be understood by the following statement:
“Suppose a function ‘g’ that operates on the function f (x) then the composition of the function would be written as [g f (x)]. This function can be renamed as h (x) = [g f (x)]”.