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Unformatted text preview: * g and g * f ? More generally, for f = ( m 1 ,b 1 ) and g = ( m 2 ,b 2 ) nd f * g and g * f . or f = ( m,b ) nd a formula for that g so that f * g = (1 , 0). Solution. g ( f ( x )) = g (3 x + 7) = 5(3 x + 7) 2 = 15 x + 33 f ( g ( x )) = f (5 x 2) = 3(5 x 2) + 7 = 15 x + 1 so f * g = (15 , 33) and g * f = (15 , 1). More generally g ( f ( x )) = g ( m 1 x + b 1 ) = m 2 ( m 1 x + b 1 ) + b 2 = m 2 m 1 x + m 2 b 1 + b 2 so f * g = ( m 1 m 2 ,m 2 b 1 + b 2 ) and, similarly, g * f = ( m 1 m 2 ,m 1 b 2 + b 1 ). Setting f * g = (1 , 0) and solving for m 2 ,b 2 we get rst m 2 = 1 m 1 and then b 2 = b 1 m 1 . We can check that setting g * f = (1 , 0) we get the same values for m 2 ,b 2 ....
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This note was uploaded on 04/01/2011 for the course MATH 101 taught by Professor Josephs during the Fall '08 term at NYU.
 Fall '08
 JOSEPHS
 Algebra

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