Function Composition Notes and examples

Composition of Functions

"plug in a function into another function"

Multiple Choice

What does

$$f\left(g\left(x\right)\right)$$  mean?

• To plug in g(x) into f(x)

• To plug in f(x) into g(x)

Multiple Choice

What does

$$g\left(f\left(x\right)\right)$$  mean?

• To plug in g(x) into f(x)

• To plug in f(x) into g(x)

Function Notation:

Plugging in a Number

Substitute the number/expression inside the parentheses in for x

Multiple Choice

find

$$f\circ g$$  

• 4x-3

• 4x+1

• 4x+3

Multiple Choice

find

$$g\circ f$$  

• 4x-1

• 4x-2

• 4x+3

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$g\left(f\left(-1\right)\right)$$  

• 2

• 15

• 7

• -9

Function Composition of Variables

• Work from the inside out

• Rather than solving for a number, you are replacing a variable with another function

• It sounds harder than it is, but it will look dumb, so be prepared for that

Multiple Choice

f(x) = 3x + 10

g(x) = x - 2

Find f(g(5))

• 19

• 23

• -10

• None of these.

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$g\left(f\left(-1\right)\right)$$  

• 2

• 15

• 7

• -9

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$f\left(g\left(3\right)\right)$$  

• 34

• 71

• 35

• 142