f(x,y) = x2 − y from Z × Z → Z. Is this function injective, bijective, surjective, or none of the former? Explain. Are the functions f(x,y) = x − y from Z × Z → Z classified as onto? Explain. Is the function f(s) = (x2 + 1)/(x2 + 2) a bijection from R to R? Explain if so, or not.
f(x,y) = x2 − y from Z × Z → Z. Is this function injective, bijective, surjective, or none of the former? Explain. Are the functions f(x,y) = x − y from Z × Z → Z classified as onto? Explain. Is the function f(s) = (x2 + 1)/(x2 + 2) a bijection from R to R? Explain if so, or not.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 58E
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Justify these answers:
- f(x,y) = x2 − y from Z × Z → Z. Is this function injective, bijective, surjective, or none of the former? Explain.
- Are the functions f(x,y) = x − y from Z × Z → Z classified as onto? Explain.
- Is the function f(s) = (x2 + 1)/(x2 + 2) a bijection from R to R? Explain if so, or not.
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