# H2 - CS123 Youssef February 2, 2010 Homework 2 Due Date:...

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CS123 February 2, 2010 Youssef Homework 2 Due Date: February 25, 2009 Problem 1: (20 points) Let R denote the set of real numbers, and Z the set of integers. Let also f : R R , g : R R , and h : Z R be 3 functions deﬁned as follows: f ( x ) = 8 x - 3 g ( x ) = 3 x 2 + 4 h ( x ) = 4 x +3 2 . a) Is f one-to-one? Onto? Prove your answer. If f is one-to-one and onto, ﬁnd f - 1 . b) Calculate g (0) , g (1) , g (2) . c) Given two sets E and F , and a function u : E F , and for every y F , deﬁne u ( y ) to be the following set: u ( y ) = { x E | u ( x ) = y } . Determine g (0) , g (4) , g (16) , g ( - 1). d) Is g one-to-one? Onto? Prove your answer. e) Is h one-to-one? Onto? Prove your answer. f) Assume now that h : R R but h has otherwise the same deﬁnition. Calculate g f ( x ) , h g ( x ) , h ( g f )( x ) , ( h g ) f ( x ).

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## H2 - CS123 Youssef February 2, 2010 Homework 2 Due Date:...

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