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!

Since the lesson includes a problem and a companion similar problem and solution. You might try this companion problem before running the solution by using the pull down MARKER TOOLS menu.

Lesson's Content

Lesson In PDF Format (no animations)

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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.

 

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