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Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}.  f: Z_(6) ->  Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) ->  Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z  ->  Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).

Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}.  f: Z_(6) ->  Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) ->  Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z  ->  Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.2: Domain And Range
Problem 59SE: Create a function in which the domain is x2 .
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Determine whether each function is an injection and determine whether each is a surjection.
The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}.
  f: Z_(6) ->  Z_(6) defined by f(x)=x^(2)+4(mod6).
 g: Z_(5) ->  Z_(5) defined by g(x)=x^(2)-11(mod5).
 h: Z*Z  ->  Z defined by h(x,y)=x+2y.
 j: R-{3} -> R defined by j(x)=(4x)/(x-3).

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