# 1140 L11 - g f

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Lecture 11: Section 1.8 Combinations of Functions Algebra of Functions Let f and g be two functions with domains A and B . We de±ne some new functions: Name De±nition Domain f ± g fg f g ex. Given f ( x ) = x 3 and g ( x ) = p x . Find each function and its domain. 1) f + g

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2) fg 3) f g Practice. If f ( x ) = p x and g ( x ) = 4 ± x 2 , ±nd the functions f ± g and f g and their domain
Composition of Functions Def. Given two functions f and g , the composi- tion of function f with function g is de±ned by ( f ± g )( x ) = The domain of ( f ± g ) is the set of x in the domain of g such that g ( x ) is in the domain of f . g f ex. Let f = x 2 and g = x ² 3. Find the functions f ± g and g ± f .

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ex. If f ( x ) = p x and g ( x ) = p 2 ± x , ±nd the following functions and their domains. 1) f ² g 2) g ² f 3) g ² g NOTE: The domain of F ( x ) = ( f ² g )( x ) is the intersection of the domain of inner function g and the resulting function F .
Practice. 1) If f ( x ) = x 3 + 5 ; and g ( x ) = p x + 3, ±nd f ( g (1)).

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## This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L11 - g f

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