## Algebra 2 Tutorial

*Function Composition*

#### Intro

Function composition is a neat little operation because it allows you to put one entire function in for another function.

#### Sample Problem

Let f(x) = 5x – 7

Let g(x) = 3x

Find f(s) and f(p)

Find f(g(x)) and g(f(x))

#### Solution

```
```**Function Composition**

####

#### Function composition is a neat little operation because it allows you to put one entire function in for another function.

####

#### Here are a couple basic function examples.

####

**Let f(x) = 5x – 7**

**Find f(s) and f(p)**

**THEN, f(s) = 5s – 7 ****AND f(p) = 5p – 7. **

**Notice that the variable "x" can be removed and changed in the notation!! f(x) can become f(s) or f(p).**

####

#### You replace your initial x variable with what you have coming as your input…in this case x is replaced by s and then by p.

#### Likewise I could have f(blob) = 5(blob) – 7. Blob has now replaced the x variable.

####

#### Now, let’s add another function g(x) = 3x. Remember ** f(x) = 5x – 7...**

####

#### Let’s say we wanted to find f(g(x)). f(g(x)) means that we will input the entire g(x) function for any x variable currently there.

####

#### So, f(g(x)) = 5(g(x)) – 7 = 5(3x) – 7 = 15x – 7

####

#### We could also find g(f(x)) which means that we will input the entire f(x) function for any x variable.

####

#### So, g(f(x)) = 3*(f(x)) = 3(5x -7) = 15x – 21

####

*NOTE:*

*-f(g(x)) does NOT mean multiply it means to put the entire g function into the f function.*

* *

*- you may also see a small open dot zero like (g o f)(x). This means g(f(x)). Likewise (f o g)(x) means f(g(x)). *

* *

*-be careful when you see a dot in between two functions. An open dot means that you need to use composition. A closed dot is multiplication!*

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