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Algebra II – Chapter 6 Day #6
Topic: Function Composition
Standards/Goals:
 F.BF.1.c.: I can use the idea of composition to evaluate radical functions.
We want to spend some time today to review how to ‘compose’ functions.
REVIEW: The composition of function g with function f is written as g ᵒ f and is defined as (g ᵒ f)(x) =
g(f(x)). The domain of g ᵒ f consists of the x-values in the domain of f for which f(x) is in the domain of g.
The same thing can be done for f(g(x))
EXAMPLES: Perform the following compositions.
Consider:
f(x) = 4x + 8
#1. Find (f ᵒ g)(x)
Consider:
h(x) = 𝟐√𝒙 + 4
#3. Find (h ᵒ p)(x)
Consider:
m(x) = 𝒙𝟐 + 𝟐
#5. Find (m ᵒ d)(x)
g(x) = -6x + 9
#2. Find (g ᵒ f)(x).
p(x) = 2x – 8
#4. Find (p ᵒ h)(x).
d(x) = 3x – 8
#6. Find (d ᵒ m)(x)
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Consider the functions:
𝒇(𝒙) = 𝟔𝒙 + √𝟔 − 𝒙
g(x) =
𝟏
𝟖 – √𝒙 −𝟏𝟏
#7. Find (f ᵒ h)(x)
#8. Find (g ᵒ h)(x)
Consider the functions:
f(x) = √𝟒𝒙 + 𝟒
g(x) = 7x + 8
h(x) = 𝟐𝒙𝟑 + 5
#9. Find (f + g).
#10. Find (f + h)
#11. Find (g + q)(x)
#12. Find (q – g)(x)
#13. Find (g – f)(x)
#14. Find (h + q)(x)
h(x) = 4x + 9
q(x) = 𝟐𝒙𝟐 + 𝟒𝒙
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HOMEWORK – Chapter 6 Day #6
Name ________________________________________ Date ________
Consider:
f(x) = 2x + 7
g(x) = -4x + 10
#1. Find (f ᵒ g)(x)
#2. Find (g ᵒ f)(x).
#3. Find f(4) + g(4)
#4. Find (f – g)(x).
Consider:
h(x) = √𝒙 + 8
p(x) = 8x – 14
#5. Find (h ᵒ p)(x)
#6. Find (p ᵒ h)(x).
#7. Find h(25)
#8. Find h(100) – p(4)
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Consider:
m(x) = 𝒙𝟐 + 𝟖
d(x) = 5x – 2
#9. Find (m ᵒ d)(x)
#10. Find (d ᵒ m)(x)
#11. Find f(-4)
#12. Find f(-10) + g(6)
Consider the functions:
𝒇(𝒙) = 𝟒𝒙 + √𝟖 − 𝒙
g(x) =
𝟏
𝟔 – √𝒙 −𝟏𝟓
#13. Find (f ᵒ h)(x)
#14. Find (g ᵒ h)(x)
Consider the functions:
f(x) = √𝟒𝒙 + 𝟒
g(x) = 7x + 8
h(x) = 𝟐𝒙𝟑 + 5
h(x) = 2x + 8
q(x) = 𝟐𝒙𝟐 + 𝟒𝒙
#15. Find f(9)
#16. Find g(-4)
#17. Find h(-4)
#18. Find q(-3)
#19. Find h(-2) + q(-2)
#20. Find g(-5) + q(0)