MAT102H5 Study Guide - Quiz Guide: Bijection, Injective Function, Mathematical Induction
71
MAT102H5 Full Course Notes
Verified Note
71 documents
Document Summary
Mat102f - intro. to mathematical proofs - fall 2018- utm. Quiz 3 solutions (version a) - november 15, 2018. You may use page 5 for rough work (not to be marked). 1: in the following examples ll in the circle that corresponds to the correct answer. 2: show that the function g : r r, g(x) = 2x+|x| is a bijection. Make sure to explain and justify your argument. Solution 1: we have two cases: g(x) = 3x if x 0, and g(x) = x if x < 0. Since they are linear functions, these give two bijections [0, ) [0, ) and ( , 0) ( , 0), and so g : [0, ) ( , 0) [0, ) ( , 0) is a bijection. If a student recognizes these properties, they get full marks. More likely, they will separately show injective and surjective, without using linear functions or unions.
