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Unformatted text preview: Two functions f and g can be composed in two ways: 1. f composed with g is written f g ( f g )( x ) = f ( g ( x )) Example: f ( x ) = x 2-4 and g ( x ) = 1-x ( f g )( x ) = 2. g composed with f is written g f ( g f )( x ) = g ( f ( x )) Example: f ( x ) = x 2-4 and g ( x ) = 1-x ( g f )( x ) = Example: Find ( f g )(2) where f and g are as given above. The domain of f g is the set of all x in the domain of g such that g ( x ) is in the domain of f . The domain of g f is the set of all x in the domain of f such that f ( x ) is in the domain of g . Example: Find the domain of f g and g f where f ( x ) = 3 x 2-1 and g ( x ) = x + 1. Decomposition of Functions: Examples: Find two functions f and g such that ( f g )( x ) = h ( x ). 1. h ( x ) = (1-x ) 3 2. h ( x ) = 4 (5 x + 2) 2...
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This note was uploaded on 01/17/2012 for the course MATH 111 taught by Professor Carolineboulis during the Fall '10 term at Lee.
- Fall '10