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Post1o4_1330 - Math 1330 Section 1.4 Combining Functions We...

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Math 1330 Class Notes – Section 1.4, Page 1 of 4 Math 1330 - Section 1.4 Combining Functions We can combine functions in any of five ways. Four of these are the familiar arithmetic operations; addition, subtraction, multiplication and division, and are very intuitive. The fifth type of combining functions is called composition of functions. In all cases, we’ll be interested in combining the functions and in finding the domain of the combined function. Suppose we have two functions, ) ( x f with domain A and ) ( x g with domain B . ( ) ( ) ( ) ( x g x f x g f + = + with domain { } B A x x ( ) ( ) ( ) ( x g x f x g f - = - with domain B A x x ( ) ( ) ( ) ( x g x f x fg = with domain B A x x ) ( ) ( ) ( x g x f x g f = with domain 0 ) ( , x g B A x x Example 1: Suppose 3 2 ) ( = x x f and 1 4 ) ( - = x x g . Find g f fg g f g f and , , - + and state the domain of each.
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Math 1330 Class Notes – Section 1.4, Page 2 of 4 Example 2: Suppose 3 2 ) ( - = x x f and 3 2 ) ( + = x x x g . Find ) 2 )( ( g f and ( 29 1 g f The final way of combining functions is called composition of functions . (
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