Function Composition Cont...

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.

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.

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)
  

​(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

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

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

​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)= ???