1.2 Composite Functions Domain and Range notes.notebook
October 26, 2011
Composite FUNctions
Domain and Range :)
From last class:
We determined that the y­value of the inner function in a composite function becomes the x­value of the outer function.
Because of this, the range of the inner function restricts the domain of the outer.
This means we cannot simply look at a composite function and determine its domain and range.
Oct 5­5:49 PM
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1.2 Composite Functions Domain and Range notes.notebook
October 26, 2011
How do we determine the domain and range??
• Determine the domain and range of the inner function.
• The DOMAIN of the composite IS the RANGE of the inner (use x instead of y of course).
• The RANGE of the composite is then determined by subbing its domain restrictions into the outer function.
Oct 5­5:53 PM
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1.2 Composite Functions Domain and Range notes.notebook
Example: Given
Determine:
October 26, 2011
and
a. f(g(x))
b. The domain and range of f(g(x)).
Oct 5­5:59 PM
3
1.2 Composite Functions Domain and Range notes.notebook
Example: Given
Determine:
October 26, 2011
and
c. g(f(x))
d. The domain and range of g(f(x)).
Oct 5­5:59 PM
4
1.2 Composite Functions Domain and Range notes.notebook
Example: Given
Determine:
October 26, 2011
and
a. f(g(x))
b. The domain and range of f(g(x)).
Oct 5­5:59 PM
5
1.2 Composite Functions Domain and Range notes.notebook
Example: Given
Determine:
October 26, 2011
and
c. g(f(x))
d. The domain and range of g(f(x)).
Oct 5­5:59 PM
6
1.2 Composite Functions Domain and Range notes.notebook
October 26, 2011
Page 86
#4 ­ find domain and range of g(f(x)) and f(g(x)).
#5a
#6a and b
(fog)(x)=f(g(x))
Oct 26­8:38 AM
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1.2 Composite Functions Domain and Range notes.notebook
October 26, 2011
Page 86 #4
Oct 26­8:50 AM
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