# lecture4 - Lecture 4 1 Lecture 4: Sec. 2.2 The Algebra of...

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Lecture 4 1 Lecture 4: Sec. 2.2 The Algebra of Functions To combine two or more functions: ex. Let f ( x ) = x - 2 and g ( x ) = 1 x - 4 . Find (include domain): 1) ( f ± g )( x ) 2) ( fg )( x )

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Lecture 4 2 For f ( x ) = x - 2 and g ( x ) = 1 x - 4 , ﬁnd (includ- ing domain): 3) ± f g ² ( x ) 4) ± g f ² ( x ) NOTE:
Lecture 4 3 Composition of Functions ex. Let h ( x ) = ( x + 4) 4 Def. Given functions f and g . The composition of f with g , written f g , is deﬁned

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Lecture 4 4 ex. For f ( x ) = x + 3 and g ( x ) = 1 x 2 , ﬁnd 1) f ( g (1)) 2) g ( f (1))
Lecture 4 5 For f ( x ) = x + 3 and g ( x ) = 1 x 2 , ﬁnd with do- main: 3) ( f g )( x ) 4) ( g f )( x )

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Lecture 4 6 Applications ex. If g ( x ) = 1 x + 2 , ﬁnd and simplify g ( a + h ) - g ( a ) h .
Lecture 4 7 ex. After t hours of operation, an assembly line can produce x ( t ) = 20 t - t 2 2 units of a product, 0 t 10. The cost of manufacturing x units of the product is C ( x ) = 100 + 50 x . a) What is the cost when the assembly line has been

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## lecture4 - Lecture 4 1 Lecture 4: Sec. 2.2 The Algebra of...

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