Function Composition Cont...

​Do Now 12/4/23

​1. Find The following Function (f+g)(x) = ???
f(x) = 3x²+2x-5 g(x) = 3x+4



2. Find the following Function (f-g)(x) = ???
f(x) = 4x+3 g(x)= 2x+5

Composition Of Function Continued...

Understanding how to use variables & operations inside the compositions.

f(g(x)) instead of f(g(#))

The Power of Composition

• Function composition is also the process of combining two or more functions to create a new function.

• We can use the different steps of operations to create a new function from two pervious functions.

• This Lesson were going to use Adding, Subtracting, Multiplying & Dividing.

Multiple Choice

What is function composition?

• The process of combining two or more functions to create a new function

• The process of breaking down complex tasks into smaller, manageable functions

• The process of reducing code duplication

• The process of promoting code readability and maintainability

Function Composition Cont...

​ f(x) = x²-5x-8
g(x) = 4x²-x+3
Find = (f + g)(x) = ???

1. We still start with the function closest to the variable.

2. Rearrange the functions to match what the function states.

3. Perform the correct order of operations to complete new function.

Multiple Choice

What is the correct set up of the functions, to start to solving for new function?

• 4x²-x+3

  • +

  • x²-5x-8

• x²-5x-8

  • +

  • 4x²-x+3

• 4x²-x+3

  =

  x²-5x-8

• x²-5x-8

  • +

  • 4x²-x+3

The Function Composition of Addition

• As We see the Function is (f o g)(x), the g function goes to the top.

• 4x²-x+3 (g)(x)

  + (operation)

• x²-5x-8 (f)(x)

• Combine like terms since we are doing addition.

• 5x²-6x-5 = (f + g)(x)
  

​Think Pair Share

​(g + f)(x) = ???

g(x) = 2x²-2x+2
f(x) = 3x-4

Function Composition Subtraction

​f(x) = 5x - 7
g(x) = 3x + 10
Find (g - f)(x)


f(x) = 5x - 7
- g(x) = 3x + 10
-----------------
(g-f)(x) = 2x+3

​Think Pair Share

​f(x) = 3x²+3x-4
g(x) = 2x²-2
Find ( g - f )(x)=???

Multiple Choice

What do we see when we Multiply two functions?

• Set Them Equal to each other

• We use the FOIL method to get new function

• To apply function g to the input x and then apply function f to the result

• To understand the properties of composite functions

Function Composition Multiplication

f(x) = 4x + 8
g(x) = x + 3,
Find f(x) ⋅ g(x) = ???
(4x +8) * (x+3)
4x²+ 12x+8x+24
4x²+20x+24

​Think Pair Share

​f(x) = 3x+3
g(x) = 2x²-4

DOL Function Composition

1. f(x) = 2x²=3x-4; g(x) = x+4; Find (f + g)(x) = ???

2. f(x) = 4x²-4x+2; g(x) = 2x²-5x; Find (f-g)(x) = ???

3. f(x) = 2x²-1; g(x) = x-4; Find (f *g)= ???