Composite Functions

What is a composite function?

• Can be thought of a series of operations

• One function is substituted into another function

• Often denoted as f(g(x)) or (f ∘ g)(x)

• Read as "f of g of x"

Example

Multiple Choice

Identify if the following is a composite function:
$$f\left(x\right)\cdot g\left(x\right)$$  

• Yes

• No

• It is an operation on functions

• You are multiplying f(x) and g(x) not substituting functions

Multiple Choice

Which expression represents g(f(x)) if

f(x) = 2x - 8 and

g(x) = 4x

• 8x - 32

• 8x² - 32x

• 8x - 8

• 6x - 8

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

• 16
• 4
• -4
• None of these.

Multiple Choice

• 136
• 4
• 8
• 147

Multiple Choice

What is f(g(3))?

• 1/8

• 8

• 1/4

• 1/2

Multiple Choice

Find f(h(5)) based on the graphs of f(x) and h(x)

• -6

• -3

• 6

• 2

Multiple Choice

• 9 - √17
• 4
• 2
• √8

Multiple Choice

Are $$\tan x^2$$ and  $$\left(\tan x\right)^2$$  the same thing?

• Yes

• No

Multiple Choice

• 8
• 3
• 2
• 0

Fill in the Blank

Find $$f\left(g\left(-2\right)\right)$$  

Multiple Choice

If f(x) = x² and g(x) = 3x - 1, find f(g(x))

• 9x² - 6x + 1

• 3x - 1

• 3x² - 1

• 9x² - 1

Multiple Choice

Given f(x)= -3x+7 and g(x)=2x² - 8, find g(f(x)).

• g(f(x))= -6x²+31
• g(f(x))= -6x²+24
• g(f(x))=18x²-84x+90
• g(f(x))=9x²-42x-41

Fill in the Blank

Find $$g\left(f\left(6\right)\right)$$  

Multiple Choice

f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))

• -42
• -26
• -18
• None of these.