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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 ).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online