### 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'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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