Business Calc Homework w answers_Part_6

Business Calc Homework w answers_Part_6 - 26 Section 1.5 x2...

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16. y 5 x 2 1 1, x $ 0 y 2 1 5 x 2 , x $ 0 ˇ y w 2 w 1 w 5 x Interchange x and y . ˇ x w 2 w 1 w 5 y f 2 1 ( x ) 5 ˇ x w 2 w 1 w or ( x 2 1) 1/2 Verify. For x $ 1 (the domain of f 2 1 ), ( f + f 2 1 )( x ) 5 f ( ˇ x w 2 w 1 w ) 5 ( ˇ x w 2 w 1 w ) 2 1 1 5 ( x 2 1) 1 1 5 x For x . 0, (the domain of f ), ( f 2 1 + f )( x ) 5 f 2 1 ( x 2 1 1) 5 ˇ ( x w 2 w 1 w 1 w ) w 2 w 1 w 5 ˇ x 2 w 5 ) x ) 5 x 17. y 5 x 2 , x # 0 x 5 2 ˇ y w Interchange x and y . y 5 2 ˇ x w f 2 1 ( x ) 5 2 ˇ x w or 2 x 1/2 Verify. For x $ 0 (the domain of f 2 1 ), ( f + f 2 1 )( x ) 5 f ( 2 ˇ x w ) 5 ( 2 ˇ x w ) 2 5 x For x # 0, (the domain of f ), ( f 2 1 + f )( x ) 5 f 2 1 ( x 2 ) 5 2 ˇ x 2 w 5 2 ) x ) 5 x 18. y 5 x 2/3 , x $ 0 y 3/2 5 ( x 2/3 ) 3/2 , x $ 0 y 3/2 5 x Interchange x and y . x 3/2 5 y f 2 1 ( x ) 5 x 3/2 Verify. For x $ 0 (the domain of f 2 1 ), ( f + f 2 1 )( x ) 5 f ( x 3/2 ) 5 ( x 3/2 ) 2/3 5 x for x $ 0, (the domain of f ), ( f 2 1 + f )( x ) 5 f 2 1 ( x 2/3 ) 5 ( x 2/3 ) 3/2 5 ) x ) 5 x 19. y 5 2 ( x 2 2) 2 , x # 2 ( x 2 2) 2 5 2 y , x # 2 x 2 2 5 2 ˇ 2 w y w x 5 2 2 ˇ 2 w y w Interchange x and y . y 5 2 2 ˇ 2 w x w f 2 1 ( x ) 5 2 2 ˇ 2 w x w or 2 2 ( 2 x ) 1/2 Verify. For x # 0 (the domain of f 2 1 ) ( f + f 2 1 )( x ) 5 f (2 2 ˇ 2 w x w ) 5 2 [(2 2 ˇ 2 w x w ) 2 2] 2 5 2 ( 2 ˇ 2 w x w ) 2 5 2 ) x ) 5 x For x # 2 (the domain of f ), ( f 2 1 + f )( x ) 5 f 2 1 ( 2 ( x 2 2) 2 ) 5 2 2 ˇ ( x w 2 w 2 w ) 2 w 5 2 2 ) x 2 2 ) 5 2 1 ( x 2 2) 5 x 20. y 5 ( x 2 1 2 x 1 1), x $ 2 1 y 5 ( x 1 1) 2 , x $ 2 1 ˇ y w 5 x 1 1 ˇ y w 2 1 5 x Interchange x and y . ˇ x w 2 1 5 y f 2 1 ( x ) 5 ˇ x w 2 1 or x 1/2 2 1 Verify. For x $ 0 (the domain of f 2 1 ), ( f + f 2 1 )( x ) 5 f ( ˇ x w 2 1) 5 [( ˇ x w 2 1) 2 1 2( ˇ x w 2 1) 1 1] 5 ( ˇ x w ) 2 2 2 ˇ x w 1 1 1 2 ˇ x w 2 2 1 1 5 ( ˇ x w ) 2 5 x For x $ 2 1 (the domain of f ), ( f 2 1 + f )( x ) 5 f 2 1 ( x 2 1 2 x 1 1) 5 ˇ x 2 w 1 w 2 w x w 1 w 1 w 2 1 5 ˇ ( x w 1 w 1 w ) 2 w 2 1 5 ) x 1 1 ) 2 1 5 ( x 1 1) 2 1 5 x 21. y 5 } x 1 2 } , x . 0
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