4.1 Composite Functions 2010
February 18, 2010
4.1 ­ Composite Functions
Objectives: Form and evaluate composite functions.
Find the domain of composite functions.
Dec 24­9:25 AM
1
4.1 Composite Functions 2010
February 18, 2010
o
Given two functions f and g, the composite function, denoted by f g, is defined by:
o
(f g)(x) = f(g(x))
Composite functions are what you get when you take the output of one function and use it for the input of the next one.
Dec 24­9:25 AM
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4.1 Composite Functions 2010
February 18, 2010
Let f(x) = x2 ­ 3x, g(x) = 3 + x, h(x) = 2√1 ­ x, k(x) = √x + 3
Find (f o g)(x)
Find (f o k)(6)
Dec 24­9:26 AM
3
4.1 Composite Functions 2010
February 18, 2010
Let f(x) = x2 ­ 3x, g(x) = 3 + x, h(x) = 2√1 ­ x, k(x) = √x + 3
o
Find (f f)(x)
o
Find (g f)(x)
Dec 24­9:26 AM
4
4.1 Composite Functions 2010
February 18, 2010
o
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.
Jan 6 ­ 11:40 AM
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4.1 Composite Functions 2010
February 18, 2010
Let f(x) = x2 ­ 3x, g(x) = 3 + x, h(x) = 2√1 ­ x, k(x) = √x + 3
o
Find (f h)(x)
o
Find the domain of (f h)(x)
Jan 6 ­ 11:38 AM
6
4.1 Composite Functions 2010
February 18, 2010
Let f(x) = x2 ­ 3x, g(x) = 3 + x, h(x) = 2√1 ­ x, k(x) = √x + 3
o
Find (h k)(x)
o
Find the domain of (h k)(x)
Jan 6 ­ 11:38 AM
7
4.1 Composite Functions 2010
February 18, 2010
Homework:
page 254
#'s: 10, 12­18 (a and b) evens, 30, 32, 34, 40, 48, 49, 54, 55, 61, 62
Jan 6 ­ 11:44 AM
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4.1 Composite Functions 2010
February 18, 2010
Feb 18­12:40 PM
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