Composition and Inverse. Relations and Functions.

Did you know that every single function, comes from other functions. You may start with f(x)= x, then go until you have a very complicated polynomial function. This is done using the composition of functions; also do you know how to get the inverse of a relation, or a function? ...mmmh..Interesting! What about the composition of a function and its inverse?

This lesson, although short is very illustrating of the composition process, and how the inverse of a relation or a function takes place. You will like the colors and animations!

Lesson's Content

Lesson's Glossary

Composite function: Combination of 2 functions where the input of the second is the output of the first.

Composition Suppose two functions f and g, where the range of g is a subset of the domain of f. Then the composition of f of g is f[g(x)].

Factoring: The process to brake a polynomial down into the product of several factors.

Factors: All whole numbers that are multiplied together to yield another number.

Factored Form: Any polynomial that is written as the product of polynomials of lower degree that may be obtained from the original polynomial.

Function: A relation of the type that has exactly one value in the domain (independent variable) matching a value in the range (dependent variable).

Function notation: A function written with the symbol f(x) instead of y. It is read as f of x.

Identity function: A function for which the input is equal to the output. In other words a function where x-coordinate is equal to the y-coordinate for all the domain of the function.

Inverse functions: Two functions are inverses if and only if both of their compositions result in the identity function. f[g(x)]=x and g[f(x)]=x.

Relation A set of ordered pairs.

Didn't you find what you were looking for? Do your search here!