domains of vector values functions

[musichael]

1. The problem statement, all variables and given/known data

r(t)- ln|t-1| i , e^t j , sqrt(t) k find the natural domains. this is a problem as an example in the book.

2. Relevant equations

It gives an answer of (-infinity,1) U (1,+infinity), (-infinity,+ininity) and [0, +infinity) and the intersection of these sets are [0,1) U (1,+infinity) then it says that the naturals domain of r(t) is 0=< t <1 or t >1

3. The attempt at a solution I understand that ln of 0 is non existant, I understand the domain of e is plus and minus infinity, i also understand the domain of the square root function, but i dont see how to find the intersection of these sets and i dont understand how they got the natural domain either. can someone please explain this to me?

[Dick]

ln(|t-1|) is only undefined at t=1. sqrt(t) is undefined for t<0. Remove those points from the number line and what's left?

[musichael]

thank you so much. I didnt realize it was that easy lol.