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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 24 and g ( x ) = 1x ( f ◦ g )( x ) = 2. g composed with f is written g ◦ f ( g ◦ f )( x ) = g ( f ( x )) Example: f ( x ) = x 24 and g ( x ) = 1x ( 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 21 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 ) = (1x ) 3 2. h ( x ) = 4 (5 x + 2) 2...
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 Fall '10
 CarolineBoulis
 Algebra, Addition, Elementary arithmetic

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