1310-Notes-Sec-36 - g f = r with domain { } A x g B x ∈...

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Math 1310 Class Notes – Section 3.6, Page 1 of 4 Math 1310 Section 3.6 Combining Functions Suppose we have two functions ) ( x f and ) ( x g . The domain of ) ( x f is the set A. The domain of ) ( x g is the set B. We can combine these two functions together in five different ways. Four basic operations Sum of Functions: ) ( ) ( ) )( ( x g x f x g f + = + with domain B A Difference of Functions: ) ( ) ( ) )( ( x g x f x g f - = - with domain B A Product of Functions: ) ( ) ( ) )( ( x g x f x fg = with domain B A Quotient of Functions: ) ( ) ( ) ( x g x f x g f = with domain { } 0 ) ( | x g B A x Example 1: Suppose 5 3 ) ( and 5 2 ) ( 2 + - = - = x x x g x x f . Find each of the following: a. ) 3 )( ( g f + b. ( 29 ) 1 ( - - g f c. ( 29 ) 0 ( fg d. ) 2 ( g f
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Math 1310 Class Notes – Section 3.6, Page 2 of 4 Composition of Functions: ( 29 )) ( ( ) ( x g f x
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Unformatted text preview: g f = r with domain { } A x g B x ∈ ∈ ) ( | Example 2: Suppose 2 ( ) 7 1and ( ) 2 5. f x x g x x x = + =--Find each of the following. a. ( 29 ) 2 ( g f r b. ( 29 (2) g f r c. ( 29 (2) f f r d. ( 29 (2) g g r Math 1310 Class Notes – Section 3.6, Page 3 of 4 e. ( 29 ) ( x g f r f. ( 29 ( ) g f x r g. ( 29 ) 1 (-f g r h. ( 29 ) ( g g r Math 1310 Class Notes – Section 3.6, Page 4 of 4 Example 3: Suppose 5 1 2 ) ( and 2 3 ) (-+ =-+ = x x x g x x x f . Find each of the following. a. ( 29 ) 4 ( g f r b. ( 29 ) 3 ( f g r Example 4: Suppose . 5 ) ( and 2 ) ( 2-= + = x x g x x f Find g f r and f g r ....
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This note was uploaded on 02/22/2012 for the course MATH 1310 taught by Professor Marks during the Summer '08 term at University of Houston.

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1310-Notes-Sec-36 - g f = r with domain { } A x g B x ∈...

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