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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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?
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