Domains of vector values functions

In summary, the conversation discusses finding the natural domains for the functions r(t)- ln|t-1| i, e^t j, and sqrt(t) k. The solution is given as (-infinity,1) U (1,+infinity), (-infinity,+infinity), and [0,+infinity), and the intersection of these sets is [0,1) U (1,+infinity). The natural domain for r(t) is 0=< t <1 or t >1. The conversation also mentions the undefined points for ln(|t-1|) and sqrt(t) and how to remove them from the number line to find the remaining natural domain.
  • #1
musichael
10
0

Homework Statement



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.

Homework 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

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 don't see how to find the intersection of these sets and i don't understand how they got the natural domain either. can someone please explain this to me?
 
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  • #2
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?
 
  • #3
thank you so much. I didnt realize it was that easy lol.
 

1. What are domains of vector values functions?

Domains of vector values functions refer to the set of all possible input values for a vector-valued function. In other words, it is the set of values that can be used as input to the function to produce a valid output.

2. How do you determine the domain of a vector-valued function?

To determine the domain of a vector-valued function, you need to look at the restrictions on the input variables. These restrictions could be due to the presence of square roots, logarithms, or fractions in the function. You also need to consider any restrictions on the variable values stated in the problem or given in the context of the function.

3. Can the domain of a vector-valued function be infinite?

Yes, the domain of a vector-valued function can be infinite. This is because the input values for a vector-valued function can range from negative infinity to positive infinity. However, there may be specific restrictions on the input values that limit the domain to a finite set of values.

4. What happens if an input value is outside the domain of a vector-valued function?

If an input value is outside the domain of a vector-valued function, the function will not produce a valid output. In other words, the function will be undefined for that particular input value. It is important to consider the domain of a function when evaluating it or solving problems involving it.

5. How can you graph a vector-valued function with a restricted domain?

To graph a vector-valued function with a restricted domain, you can use a graphing calculator or software that allows you to specify the domain of the function. You can also manually plot points on a graph by selecting values within the domain and calculating the corresponding output values. It is important to remember that a restricted domain can change the shape and features of the graph of a vector-valued function.

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