Unformatted text preview: 5 2 x 1 3 y 2 3 5 2 x } y 2 2 3 } 5 x Interchange x and y . } x 2 2 3 } 5 y f 2 1 ( x ) 5 } x 2 2 3 } . Verify. ( f + f 2 1 )( x ) 5 f 1 } x 2 2 3 } 2 5 2 1 } x 2 2 3 } 2 1 3 5 ( x 2 3) 1 3 5 x ( f 2 1 + f )( x ) 5 f 2 1 (2 x 1 3) 5 } (2 x 1 2 3) 2 3 } 5 } 2 2 x } 5 x 14. y 5 5 2 4 x 4 x 5 5 2 y x 5 } 5 2 4 y } Interchange x and y . y 5 } 5 2 4 x } f 2 1 ( x ) 5 } 5 2 4 x } Verify. ( f + f 2 1 )( x ) 5 f 1 } 5 2 4 x } 2 5 5 2 4 1 } 5 2 4 x } 2 5 5 2 (5 2 x ) 5 x ( f 2 1 + f )( x ) 5 f 2 1 (5 2 4 x ) 5 } 5 2 (5 4 2 4 x ) } 5 } 4 4 x } 5 x 15. y 5 x 3 2 1 y 1 1 5 x 3 ( y 1 1) 1/3 5 x Interchange x and y . ( x 1 1) 1/3 5 y f 2 1 ( x ) 5 ( x 1 1) 1/3 or ˇ 3 x w 1 w 1 w Verify. ( f + f 2 1 )( x ) 5 f ( ˇ 3 x w 1 w 1 w ) 5 ( ˇ 3 x w 1 w 1 w ) 3 2 1 5 ( x 1 1) 2 1 5 x ( f 2 1 + f )( x ) 5 f 2 1 ( x 3 2 1) 5 ˇ 3 ( x w 3 w 2 w 1 w ) w 1 w 1 w 5 ˇ 3 x 3 w 5 x Section 1.5 25...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN

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