April 4th, 2017, 07:58 PM  #1 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  state the domain of the following use set notation and interval notation
state the domain of the following...thanks I am so clueless f(x)=x 
April 4th, 2017, 08:13 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,921 Thanks: 534 
Well that's a good question. What number system are we working in? All things being equal, you are probably working in the real numbers. The variable $x$ often stands for a real number. So I'd guess that the domain is the reals. But the function $f(x) = x$ is the identity function that returns whatever value is input to it; and there is an identity function on every set there is. For example there is an identity function on the natural numbers that would typically be denoted as $f(n) = n$. But the use of $x$ or $n$ is only a general convention and can't always be relied on. Maybe $n$ is an integer rather than a natural number. So the real answer is that you have to supply more information to determine the definitive answer. 
April 4th, 2017, 08:24 PM  #3  
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  Quote:
 
April 4th, 2017, 09:22 PM  #4  
Senior Member Joined: Aug 2012 Posts: 1,921 Thanks: 534  Quote:
 
April 4th, 2017, 09:25 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1618 
The symbol ℝ or $\small\mathbb{R}$ is used to denote the set of all reals.

April 4th, 2017, 10:14 PM  #6 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10 
I don't want to people to get upset so not sure what I would look up to find out more but how can these following questions be answered if it seems we don't have anything to plug in for x? so would the square root of x1 be (1,oo)?

April 4th, 2017, 10:25 PM  #7  
Senior Member Joined: Aug 2012 Posts: 1,921 Thanks: 534  Quote:
Also the way you wrote it, we can't tell if you mean $\sqrt{x  1}$ or $\sqrt{x}  1$, which is different. You can write sqrt(x  1) or sqrt(x)  1, depending on which one you mean. But writing it out in English without parentheses is ambiguous. Last edited by Maschke; April 4th, 2017 at 10:30 PM.  
April 4th, 2017, 10:40 PM  #8  
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  Quote:
 
April 4th, 2017, 11:42 PM  #9 
Senior Member Joined: Aug 2012 Posts: 1,921 Thanks: 534  
April 4th, 2017, 11:49 PM  #10 
Senior Member Joined: Feb 2016 From: seattle Posts: 377 Thanks: 10  

Tags 
domain, interval, notation, set, state 
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