assn3t - CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER...

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Unformatted text preview: CONCORDIA UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE & SOFTWARE ENGINEERING COMP 232/2 Mathematics for Computer Science FALL 2010 Assignment 3 1. Let a, b, c ∈ R with b 6 = ac and let the function f : R → R be given by f ( x ) = 8 < : a if x = c, ax- b x- c if x 6 = c. i) Show that f is one-to-one. ii) Show that f is onto. iii) Find f- 1 ( y ). 2. For sets A , B , and S , with S ⊆ B , and a function f : A → B , we define f- 1 ( S ) = ˘ a ∈ A : f ( a ) ∈ S ¯ . For each of the following find f- 1 ( S ). A B f S i) R R x 7→ x- b x c { y : 0 < y < 1 } ii) R R x 7→ x 3- 7 x + 16 { y : 10 ≤ y ≤ 22 } iii) R R × R t 7→ (cos t, sin t ) { ( x, y ) : x < 0, y > } 3. Let x be a real number. i) Prove that b- x c =-d x e and d- x e =-b x c . ii) Give a proof by cases that ¨ 4 x ˝ = ¨ x ˝ + ¨ x + 1 4 ˝ + ¨ x + 1 2 ˝ + ¨ x + 3 4 ˝ . 4. Let a and b be relatively prime positive integers....
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This note was uploaded on 11/15/2010 for the course ENCS COMP 232 taught by Professor Ford during the Fall '10 term at Concordia University Irvine.

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