- #1
kingwinner
- 1,270
- 0
Question 1)
{(u1,u2) : -∞ < (u1+u2)/2 < ∞ and -∞ < (u1-u2)/2 < ∞ } = {(u1,y2) : -∞ < u1 < ∞ and -∞ < u2 < ∞}
Why is the equality(=) true? How can I see that the two sets describe the same region?
Question 2)
2) Define u1=y1+y2, u2=y1-y2, so the mapping (or function) is (u1,u2)=f(y1,y2)=(y1+y2,y1-y2). If -∞ < y1 < ∞ and -∞ < y2 < ∞ are the DOMAIN of this mapping, then this implies the RANGE is -∞ < u1 < ∞ and -∞ < u2 < ∞. WHY?
Can someone explain, please? Any help would be appreciated!
{(u1,u2) : -∞ < (u1+u2)/2 < ∞ and -∞ < (u1-u2)/2 < ∞ } = {(u1,y2) : -∞ < u1 < ∞ and -∞ < u2 < ∞}
Why is the equality(=) true? How can I see that the two sets describe the same region?
Question 2)
2) Define u1=y1+y2, u2=y1-y2, so the mapping (or function) is (u1,u2)=f(y1,y2)=(y1+y2,y1-y2). If -∞ < y1 < ∞ and -∞ < y2 < ∞ are the DOMAIN of this mapping, then this implies the RANGE is -∞ < u1 < ∞ and -∞ < u2 < ∞. WHY?
Can someone explain, please? Any help would be appreciated!
Last edited: