1310-Notes-Sec-36-big-filled

1310-Notes-Sec-36-big-filled - ( 29 ( ) ( ( )) f g x f g x...

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Math 1310 Class Notes – Section 3.6, Page 1 of 9 Math 1310 Section 3.6 Combining Functions Suppose we have two functions ( ) f x and ( ) g x . The domain of ( ) f x is the set A. The domain of ( ) g x is the set B. We can combine these two functions together in five different ways. Four basic operations Sum of Functions: ( )( ) ( ) ( ) f g x f x g x + = + with domain A B Difference of Functions: ( )( ) ( ) ( ) f g x f x g x - = - with domain A B Product of Functions: ( )( ) ( ) ( ) fg x f x g x = with domain A B Quotient of Functions: ( ) ( ) ( ) f f x x g g x = with domain { } | ( ) 0 x A B g x
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Math 1310 Class Notes – Section 3.6, Page 2 of 9 Example 1: Suppose 2 ( ) 2 5 and ( ) 3 5 f x x g x x x = - = - + . Find each of the following: a. ( )(3) f g + b. ( 29 ( 1) f g - -
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Math 1310 Class Notes – Section 3.6, Page 3 of 9 c. ( 29 (0) fg d. (2) f g
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Math 1310 Class Notes – Section 3.6, Page 4 of 9 Composition of Functions:
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Unformatted text preview: ( 29 ( ) ( ( )) f g x f g x = r with domain { } | ( ) x B g x A Example 2: Suppose 2 ( ) 7 1and ( ) 2 5. f x x g x x x = + =--Find each of the following. a. ( 29 (2) f g r b. ( 29 (2) g f r Math 1310 Class Notes Section 3.6, Page 5 of 9 c. ( 29 (2) f f r d. ( 29 (2) g g r Math 1310 Class Notes Section 3.6, Page 6 of 9 e. ( 29 ( ) f g x r f. ( 29 ( ) g f x r Math 1310 Class Notes Section 3.6, Page 7 of 9 g. ( 29 ( 1) g f-r h. ( 29 (0) g g r Math 1310 Class Notes Section 3.6, Page 8 of 9 Example 3: Suppose 3 2 1 ( ) and ( ) 2 5 x x f x g x x x + + = =--. Find each of the following. a. ( 29 (4) f g r b. ( 29 (3) g f r Math 1310 Class Notes Section 3.6, Page 9 of 9 Example 4: Suppose 2 ( ) 2 and ( ) 5. f x x g x x = + =-Find f g r and g f r ....
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1310-Notes-Sec-36-big-filled - ( 29 ( ) ( ( )) f g x f g x...

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