12 Function Composition 092216.notebook
September 25, 2016
TBLS IB Math HL Year One
9/22/16 AIM: DWBAT compose and decompose functions and find the domain of a composite function.
1.2
Warm Up: HW: Ex. 2.2 (p. 60) #3, 5, 7, 11, 14, 15, 21
Sep 212:36 PM
Warm Up
Which is the "inner" (first) function in (f ∘ g)(x)? Which is the "outer" (second) function? What about for (f ∘ g ∘ h)(x)? Does (f ∘ g)(x) = (g ∘ f)(x) in general? What happens when they are equal?
Sep 249:28 PM
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12 Function Composition 092216.notebook
September 25, 2016
Decomposing Functions
Sep 249:28 PM
Domain of Composite Functions What is (f ∘ g)(x)?
o f g
g
x
f g(x)
g
f(g(x)
g f
f
Sep 249:28 PM
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12 Function Composition 092216.notebook
September 25, 2016
Domain of Composite Functions Consider f(x) = x2 and g(x) = √x. What is the domain of f(x)? What is the domain of g(x)? What is (f ∘ g)(x)? What is the domain of (f ∘ g)(x)?
Sep 249:28 PM
Domain of Composite Functions
f(g(x)) = x
Sep 249:28 PM
3
12 Function Composition 092216.notebook
September 25, 2016
Domain of Composite Functions For a value x to be in the domain of (f ∘ g)(x), two things need to be true: 1. the value x exists in the domain of g 2. the value g(x) exists in the domain of f
f(g(x)) = x
Sep 249:28 PM
Domain of Composite Functions
Sep 249:28 PM
4
12 Function Composition 092216.notebook
September 25, 2016
Homework HW: Ex. 2.2 (p. 60) #3, 5, 7, 11, 14, 15, 21
Sep 249:28 PM
Homework HW: Ex. 2.2 (p. 60) #3, 5, 7, 11, 14, 15, 21
Answers:
Sep 249:28 PM
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