This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Rev.S08 MAC 1105 Module 6 Composite Functions and Inverse Functions 2 Rev.S08 Learning Objectives Upon completing this module, you should be able to: 1. Perform arithmetic operations on functions. 2. Perform composition of functions. 3. Calculate inverse operations. 4. Identity onetoone functions. 5. Use horizontal line test to determine if a graph represents a onetoone function. 6. Find inverse functions symbolically. 7. Use other representations to find inverse functions. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 Rev.S08 Composite Functions and Inverse Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Combining Functions; Composite Functions Combining Functions; Composite Functions Inverse Functions Inverse Functions There are two major topics in this module: 2 4 Rev.S08 Five Ways of Combining Functions If If f ( x ) and ) and g ( x ) both exist, the sum, difference, ) both exist, the sum, difference, product, quotient and composition of two functions product, quotient and composition of two functions f and and g are defined by are defined by ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. ( ) ( ) ( ) ( ) )) ( ( ) ( ) ( where ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( x g f x g f x g x g x f x g f x g x f x fg x g x f x g f x g x f x g f = ! = " # $ % & ’ ( = ) = ) + = + o 5 Rev.S08 Example of Addition of Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Let Let f ( x ) = ) = x 2 2 + 2 + 2 x and and g ( x ) = 3 ) = 3 x 1 1 Find the symbolic representation for the function Find the symbolic representation for the function f f + + g and use this to evaluate ( and use this to evaluate ( f f + + g )(2). )(2). ( f + g )( x ) = ( x 2 2 + 2 + 2 x ) + ( 3 x − 1) 1) ( f + g )( x ) = x 2 2 + 5 + 5 x − 1 1 ( f + g )(2) = 2 2 2 + 5( + 5(2) − 1 = 13 1 = 13 or or ( ( f f + + g )(2) = )(2) = f (2) + (2) + g (2) (2) = 2 = 2 2 2 + 2(2) + 3(2) + 2(2) + 3(2) − 1 1 = 13 = 13 6 Rev.S08 Example of Subtraction of Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Let Let f ( x ) = ) = x 2 2 + 2 + 2 x and and g ( x ) = 3 ) = 3 x − 1 1 Find the symbolic representation for the function f − g and use this to evaluate ( f − g )(2). ( f − g )( x ) = ( x 2 2 + 2 + 2 x ) − ( 3x 3x − 1) 1) ( f − g )( )( x ) = ) = x 2 2 − x + 1 + 1 So So ( f − g )(2) = 2 2 2 − 2 + 1 = 3 + 1 = 3 3 7 Rev.S08 Example of Multiplication of Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Let Let f ( x ) = ) = x 2 2 + 2 + 2 x and and g ( x ) = 3 ) = 3 x − 1 1 Find the symbolic representation for the function fg and use this to evaluate ( fg )(2) ( fg )( x ) = ( x 2 2 + 2 + 2 x ) ( 3 x − 1) 1) ( fg )( x ) = 3 x 3 3 + 6 + 6 x 2 − x 2 − 2 2 x ( fg )( x ) = 3 x 3 3 + 5 + 5 x 2 2 − 2 2 x So So (fg)(2) = 3(2) 3(2) 3 3 +5(2) +5(2) 2 2 − 2(2) = 40 2(2) = 40...
View
Full Document
 Summer '07
 RUSSEL
 Algebra, Inverse Functions, Composite Functions, Inverse function, Injective function, Function composition, Click Link, Subtraction of Functions

Click to edit the document details