# Domain and Range using sets

1. Sep 18, 2007

### Feldoh

I was just wondering if you could write a functions domain and range with a set?

Would it be something like

D: {$$x \epsilon \mathbb{R}$$ | any condtitions}
R: {$$f(x) \epsilon \mathbb{R}$$ | any condtitions}

for any function f(x)?

2. Sep 18, 2007

What exactly is your question? Look at the definitions of "domain" and "range" (of a function). Of course they are sets. And of course that, in the definition of "range", some conditions must be satisfied, namely, R(f) = {f(x) : x is in the domain of f}.

3. Sep 18, 2007

### Diffy

His question is simple, Can you write the domain and range of a function as sets. The answer is Yes, because they are sets.

4. Sep 18, 2007

### Feldoh

Thanks for the replies. I know that the domain and range are sets, I was more asking along the lines of is my set "notation" correct? Sorry, I should have asked that to begin with...

5. Sep 19, 2007

### HallsofIvy

Staff Emeritus
Should have asked what? If you know that "domain" and "range" of a function are sets, then of course they can be written in "set notation"!

6. Sep 19, 2007

### JonF

You don’t need to put “any condition” - the vertical bar should read “such that” so when you write a set ask yourself is what you wrote makes sense saying "such that" for |. Also you could just put R for your example of domain. If you gave the set you gave as range for an answer you should get 0 points. When a book ask you to find the range they are asking for the range specific to that function; yours just trys to restate the definition.

Typically they will look something like

R-{0} or something like {x | x >= 0 and x is an element of R}