Composite Functions Lesson

​Composite Functions

Dr. Tom Giles

Function Composition Review

Multiple Choice

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

• 11x² - 1
• 5x⁴ + 6x² - 1
• 5x² + 6x - 1
• 5x² + 8x - 1

Multiple Choice

Given
 f(x) = 2x² + 5x - 17,
find f(-1). 

• f(-1) = -20
• f(-1) = -24

Multiple Choice

f(x)= x+3

g(x)= x-2

Find (g(x) / f(x))

Be careful!!

• (x + 3)/(x - 2)

• (x - 2)/(x + 3)

• -2/3

• 3/2

• It is an operation on functions

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

Multiple Choice

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

• Yes

• No

Multiple Choice

Which one is the same as fοg(x)

• g(f(x))

• f(g(x))

Multiple Choice

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

• x²+2x+3
• 4x²+3
• 2x²+3
• 2x²+6

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

Given f and g in the graph,

what is (f ° g)(-1) ?

• 1

• 4

• -1

• 6

Multiple Choice

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

Function Composition (Equations)

Multiple Choice

f(x) = 3x + 10

g(x) = x - 2

Find f(g(5))

• 19

• 23

• -10

• None of these.

Multiple Choice

p(x) = 3x + 4

q(x) = 2x²

Find p(q(x))

• 10x²

• 18x² + 4

• 6x² + 4

Multiple Choice

f(x)=x²-4

h(x)=3x+3

f(h(x))

• 3x²-9

• 12x²+8x+5

• 16x²-36x+20

• 9x²+18x+5