0-6: Operations on and Composition of Functions Define the sum, difference, product, quotient and...
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0-6: Operations on and Composition of Functions • Define the sum, difference, product, quotient and composition of functions Objectives: ©2002 Roy L. Gover ([email protected])
Transcript of 0-6: Operations on and Composition of Functions Define the sum, difference, product, quotient and...
0-6: Operations on and Composition of Functions
• Define the sum, difference, product, quotient and composition of functions
Objectives:
©2002 Roy L. Gover ([email protected])
Operations
f g x f x g x
Functions: ( ), ( )f x g x
f g x f x g x
Sum:
Given:
Domain:
Difference:Domain: domain of f(x) domain of g(x)x
domain of f(x) domain of g(x)x
Operations cont .
f g x f x g x
/ /f g x f x g x
Product:Domain:
Quotient:Domain: domain of f(x) domain of g(x), g(x) 0x
domain of f(x) domain of g(x)x
ExampleExample: Given f and g as follows:
1( ) ( ) 3f x g x x
x
Find each of the following and determine the domain of the resulting function.
a.) (f + g)(x)b.) (f - g)(x)c.) (f · g)(x)
d.) (f / g)(x)
Composition
Given: Two function f and g, the composite function, is defined by:
xgfxgf )(
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.
Example
Example: Given the functions f and g, find f ○ g and the domain of f ○ g.
2
1)()(
xxgxxf
