Let f(x,y)= √ (y2−x2) be a function of two variables, the domain of f is given by the set: Dom f = { (x,y) ∈ R2 ∣ (y−x) (y+x) ≥0 } Consider the following statements. 1. Let x ∈ R be such that (x,1) ∈ Dom f, then we can say that for all y ∈ R the point (1, xy ) ∈ Dom f. 2. Let a,b ∈ R be such that (0,a),(b,−b) ∈ Dom f, then it can be stated that [(0,a)+(b,−b)] ∈ Dom f. Which is correct, incorrect or both?

Let f(x,y)= √ (y2−x2) be a function of two variables, the domain of f is given by the set: Dom f = { (x,y) ∈ R2 ∣ (y−x) (y+x) ≥0 } Consider the following statements. 1. Let x ∈ R be such that (x,1) ∈ Dom f, then we can say that for all y ∈ R the point (1, xy ) ∈ Dom f. 2. Let a,b ∈ R be such that (0,a),(b,−b) ∈ Dom f, then it can be stated that [(0,a)+(b,−b)] ∈ Dom f. Which is correct, incorrect or both?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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