Inverse and composite function
Introduction
An inverse function is a function that undoes the action of the function. A function gg is the inverse of a function ff if whenever y=f(x)y=f(x) then x=g(y)x=g(y). In other words, applying ff and then gg is the same thing as doing nothing. We can write this in terms of the composition of ff and gg as g(f(x))=xg(f(x))=x. On the other hand, the composite function is a function of a different function. It is often created when one function is replaced into an alternative function. It is termed as the function of a function, and it is denoted by ᴏ. The composite and inverse function is an essential element of mathematics. An inverse function is normally denoted by f-1 (x) is defined as the inverse function of f(X), which is the common form of a question of f and X if it is consistently reverse the f(x) processes. In order to accommodate these concepts in mind, the essential concepts needed to be accommodated include the concept of the binary operation concept, proportionally, similarity, and geometry.
Some of the simple concept of the composite and the inverse that I can image include the most straightforward question that translates one function into another function. An example of the purest form of the composite function includes; It, therefore, means that in a mathematical case where f(x) turns in a and b, then the inverse function f-1 (x) must also turn in a and be. More concisely and formally, f-1 (x) is considered the inverse function of F(X) If f (f-1 (x)) =x. An example of the simplest composite of the composite function is;the composite function is therefore written as (f ᴏ g(x) = f (g(X)).
Example in daily life
The inverse and composite functions are concepts that are very common in daily life. Most of the daily human activities fall between these two concepts. In everyday life, some actions can be interpreted as the inverse function. An example of an inverse function in life could, in the way we tie our shoe laces. In whatever way one matches the shoelace the result is a tied shoelace which services the same purpose
An example of a composite function in real life in a team situation each player of 11 players has name and number. Therefore each player’s name and number can be termed as a composite function since they save the same service calling the payer by the name or number is the same thing since they both represent the same thing. The number, for example, if number 9 is Messy, then one substituting 9 when refereeing to that particular player, with the name messy is a situation of a composite function.
Graphs
The strategy used in obtaining graph of the inverse function is derived from the graph of f(x) by switching the position of the x and the y-axis. This is also the same as reflecting graph across the diagonal line through of y=x over the origin of the graph. Therefore, development of a developing an inverse graph is a factor of one function and it obtained by multiplying the chart with the fact of mapping for example if the element is two then the graph of the composite function is obtained by multiplying the by coordinates by 2