# Find the domain of the function

• miglo
In summary, I am confused about whether the domains for the first and second functions are open or closed. I think the domains for the first function are closed, but I'm not sure. The domain for the second function is open, but I'm not sure if it's open everywhere or just at the origin.
miglo

## Homework Statement

so I am supposed to find the domain of the function, the range, describe its level curves, find the boundary of the functions domain, determine if the boundary is an open region, a closed region, or neither, and decide it the domain is bounded or unbounded.
f(x,y)=sqrt(y-x)
and f(x,y)=xy

## The Attempt at a Solution

ive found the domains and range for the function, described the level curves and found the boundary of the domain for the first function but what is really confusing me is whether the domain is open of closed.
for the first one the domain is all points in the xy-plane such that y is greater than or equal to x, at first i thought the domain was closed but some tutors told me that its actually open and closed. can anyone explain this to me as the tutors themselves did not know how to explain it.
for the second function i know the domain is all points in the xy-plane, i went ahead and took a peak at the answers and it says the domain is open and closed, i don't understand this, my first guess was that it was just open but i was wrong
my professor never mentioned that it could be both open and closed, so i don't understand it

miglo said:

## Homework Statement

so I am supposed to find the domain of the function, the range, describe its level curves, find the boundary of the functions domain, determine if the boundary is an open region, a closed region, or neither, and decide it the domain is bounded or unbounded.
f(x,y)=sqrt(y-x)
and f(x,y)=xy

## The Attempt at a Solution

ive found the domains and range for the function, described the level curves and found the boundary of the domain for the first function but what is really confusing me is whether the domain is open of closed.
for the first one the domain is all points in the xy-plane such that y is greater than or equal to x, at first i thought the domain was closed but some tutors told me that its actually open and closed. can anyone explain this to me as the tutors themselves did not know how to explain it.
The domain of the first function is the half-plane consisting of the line y = x and all of the points above this line. Since the boundary of this set is the line y = x, and the boundary is part of the set, the domain is closed. See http://en.wikipedia.org/wiki/Closed_set.

Per the article, the set [1, ∞) in R is closed, and from this we can reasonably conclude that {(x, y) | y ≥ x} is also closed. On the other hand, the set [0, 1) is neither open nor closed.

Some sets are both open and closed; e.g., the real line (-∞, ∞) and the plane R2.
miglo said:
for the second function i know the domain is all points in the xy-plane, i went ahead and took a peak at the answers
I think you took a peek at the answers. Peaks are generally too large to take.
miglo said:
and it says the domain is open and closed, i don't understand this, my first guess was that it was just open but i was wrong
my professor never mentioned that it could be both open and closed, so i don't understand it

thanks!

and yeah i took a peek not a peak haha

Or you could say, in a fit of pique you took a peek at the peak.

## 1. What is the domain of a function?

The domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of values that can be plugged into the function to get an output.

## 2. How do I find the domain of a function?

To find the domain of a function, you need to determine which values are allowed to be input into the function. This can be done by looking for any restrictions, such as division by zero or taking the square root of a negative number.

## 3. Are there any common restrictions when finding the domain of a function?

Yes, there are a few common restrictions when finding the domain of a function. These include division by zero, taking the square root of a negative number, and taking the logarithm of a negative number.

## 4. What happens if I plug in a value that is not in the domain of a function?

If you plug in a value that is not in the domain of a function, the function will not be defined for that input. This means that you will not get an output or a solution to the function.

## 5. Can the domain of a function be expressed in interval notation?

Yes, the domain of a function can be expressed in interval notation. This is a way of representing a set of numbers using inequalities. For example, if the domain of a function is all real numbers greater than or equal to 2, it can be expressed as [2, ∞).

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