My Math Forum state the domain of the following use set notation and interval notation

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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. Thanks from Joppy and GIjoefan1976
April 4th, 2017, 08:24 PM   #3
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 Originally Posted by Maschke 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.
Hello thanks for your time...I think I saw my teacher use something that looked the pi symbol but had it kinda like this if they were connected TR have you seen this? so would the interval be (-oo,oo) and then the set the symbol for real numbers? he also said not to divide by 0 and don't take the even root of a negative number

April 4th, 2017, 09:22 PM   #4
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 Originally Posted by GIjoefan1976 Hello thanks for your time...I think I saw my teacher use something that looked the pi symbol but had it kinda like this if they were connected TR have you seen this? so would the interval be (-oo,oo) and then the set the symbol for real numbers? he also said not to divide by 0 and don't take the even root of a negative number
$\mathbb R$? That's the real numbers. $(-\infty, ~~\infty)$ is another notation for the real numbers. Sounds like you're working in the real numbers.

 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. Thanks from GIjoefan1976
 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 x-1 be (-1,oo)?
April 4th, 2017, 10:25 PM   #7
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 Originally Posted by GIjoefan1976 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 x-1 be (-1,oo)?
In order to take the square root of $x - 1$ we must have $x - 1 \geq 0$ or $x \geq 1$. So the domain is $[1, ~\infty)$. Does that make sense?

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
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 Originally Posted by Maschke In order to take the square root of $x - 1$ we must have $x - 1 \geq 0$ or $x \geq 1$. So the domain is $[1, ~\infty)$. Does that make sense? 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.
okay sorry, the way they have it, it is g(x)=sqrt(x-1)

April 4th, 2017, 11:42 PM   #9
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 Originally Posted by GIjoefan1976 okay sorry, the way they have it, it is g(x)=sqrt(x-1)
Do you see why the domain is anything greater than or equal to 1?

April 4th, 2017, 11:49 PM   #10
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 Originally Posted by Maschke Do you see why the domain is anything greater than or equal to 1?
thank you for asking, I think I do because the x is positive, and even though it says negative it would still be 1 since it's one space no matter which way we go?

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