# Quick easy question to make sure i got this

1. Oct 22, 2004

### Gecko

does the domain of $$f(x) = \sqrt {x-1}$$ equal $$dom(f) = (1,\infty)$$? if wrong, can you tell me what i did wrong? thanks.

2. Oct 22, 2004

### Tide

x = 1 would be included.

3. Oct 22, 2004

### Muzza

f is (presumably) a function into R, and then taking any subset of [1, inf) as its domain will also work. However, if you set f's codomain equal to C (the complex numbers), then its domain could be any subset of R or C... It doesn't seem like a particularly well-posed question.

4. Oct 22, 2004

### Gecko

the question was exactly "What is the domain of $$f(x) = \sqrt {x-1}$$?" so the answer is $$dom(f) = [1, \infty)$$? and its in the very begginning of the book so i dont think it would go into complex numbers (seeing as i have no idea what they are) i just wanted to make sure i was understanding the material up to this point.

oh yeah, does [x,y) mean the the domain can be equal to or greater than x and greater than y, or is it less than y? and (x,y) means that its greater than x and y or just less than y? i was confused with this in the book as well (wish the answers where in the back >.<)

Last edited: Oct 22, 2004
5. Oct 22, 2004

### arildno

Your book is very sloppy in asking this (along with most other books).
What it should have said is:

(Given that the value of f should be a real number), What is the MAXIMAL domain we can assign to this function?
The parenthesized condition might be dropped.

6. Oct 24, 2004

### Leaping antalope

[x, y) means that the domain is equal to or greater than x, but less than y.
(x, y) means that the domain is greater then x but less than y.

7. Oct 24, 2004

### matt grime

It isn't a well posed question. In fact it is an abhorrently incorrect question that makes many of us of the 'pure' persuasion want to commit murder. However, it is also a very common [kind of] question, and one must always append the words: where the function is considered as a subset of RxR, and the domain is maximal with respect to this property.

(Not for the digestion of the OP, but perhaps for Muzza: the domain could be taken as any algebraically closed field, and seeing as no range is specified at all even that is assuming too much. The domain and Range are part of the definition of the function and should not be omitted. But that doesn't stop every calc/pre-calc course I've seen doing this.)