Cha8 - Chapter 8 Joy Zhou 10-28-2009 Chapter 8 8.1, 8.2,...

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Unformatted text preview: Chapter 8 Joy Zhou 10-28-2009 Chapter 8 8.1, 8.2, 8.3, 8.4, 8.6, 8.8 8.1 (a) h ( f ( t )) = | t- 1 | = braceleftBigg t- 1 if t ≥ 1 1- t if t < 1 (1) (c) h ( h ( t )- 1) = || t | - 1 | = braceleftBigg | t- 1 | t ≥ | - t- 1 | t < = t- 1 t ≥ 1 1- t ≤ t < 1- t- 1 t ≤ - 1 t + 1- 1 < t < (2) 8.3 Note: notice the difference between part (a) and part (b). If you see these types of problems in the second mid term, please pay attention not to misunderstand the problem. (a) f ( f ( x )) = a ( ax + b ) + b (3) = a 2 x + ( ab + b ) (4) (b) Different from part (a), where f ( x ) is given, here g ( g ( x )) is given and you are asked to find g ( x ). An untold trick is to guess that g ( x ) is a linear function. 1 Suppose g ( x ) = ax + b . Our goal is to figure out the coefficients a and b . Then g ( g ( x )) can also be written in terms of a, b and x as g ( g ( x )) = a 2 x + ( ab + b ) ....
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This note was uploaded on 12/23/2009 for the course GEN GEN STUDIE taught by Professor Kellyshonttell during the Fall '09 term at University of Washington.

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Cha8 - Chapter 8 Joy Zhou 10-28-2009 Chapter 8 8.1, 8.2,...

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