Function Composition

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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