4.1 composite functions 2011 - poudre school district · 4.1 composite functions 2011 subject:...
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4.1 Composite Functions 2011
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April 18, 2011
4.1 Composite Functions
Objectives: Form and evaluate composite functions. Find the domain of composite functions.
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Warmup:Let f(x) = x2 3x, g(x) = 3 + x, h(x) = 2√1 x, k(x) = √x + 3
1. f(4) 2. g(5)
3. h(8) 4. k(22)
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4.1 Composite Functions 2011
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Composite functions are what you get when you take the output of one function and use it for the input of the next one.
Given two functions f and g, the composite function, denoted by f g, is defined by:
o
(f g)(x) = f(g(x))o
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Find (f g)(x)
Let f(x) = x2 3x, g(x) = 3 + x, h(x) = 2√1 x, k(x) = √x + 3
Find (f k)(6)oo
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Find (f f)(x)oFind (g f)(x)o
Let f(x) = x2 3x, g(x) = 3 + x, h(x) = 2√1 x, k(x) = √x + 3
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The domain of f g is the set of all numbers x in the domain of g such that g(x) is in the domain of f.
o
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Let f(x) = x2 3x, g(x) = 3 + x, h(x) = 2√1 x, k(x) = √x + 3
Find (f h)(x)o Find the domain of (f h)(x)o
![Page 8: 4.1 Composite Functions 2011 - Poudre School District · 4.1 Composite Functions 2011 Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook](https://reader033.vdocument.in/reader033/viewer/2022053018/5f1f794059640e377f41c6a5/html5/thumbnails/8.jpg)
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Let f(x) = x2 3x, g(x) = 3 + x, h(x) = 2√1 x, k(x) = √x + 3
Find (h k)(x)o Find the domain of (h k)(x)o
![Page 9: 4.1 Composite Functions 2011 - Poudre School District · 4.1 Composite Functions 2011 Subject: SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook](https://reader033.vdocument.in/reader033/viewer/2022053018/5f1f794059640e377f41c6a5/html5/thumbnails/9.jpg)
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Homework:page 254#'s: 10, 1218 (a and b) evens, 30, 32, 34, 40, 48, 49, 54, 55, 61, 62