Domain of a function - f(x,y)=root(1-x)+root(1-y)

In summary, the domain for the given function is x and y values between negative infinity and 1, and when graphed on the x-y plane, the domain is the intersection of the domains of x and y. The function can also be considered a 2D problem unless stated otherwise and the graph is a sideways parabola ending at z=0, with x and y both being less than or equal to negative one.
  • #1
FOIWATER
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I have came up with a solution for this - in order for this function to be defined, we must have an x and y between negative infinity up to and including the number 1.

If asked to graph this domain, does the domain lie on the x-y plane of three dimensional space, and is it the intersection of the domains of x and y?

I know the only sensible way to my question will likely go over my head - I Just started vector calculus - so no worries, I find it difficult for this to make sense to me.

I am thinking of the domain as the values "under" the z-plane in 3d space, if that makes any sense... at all - or above! or maybe a point in three-d space is ON the plane, when z is zero?
 
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  • #2
i think this is simplay a 2D problem in x and y unless you want to make it 3D by stating f(x,y)=z

next what does the root(1-x) mean? I don't understand how to even plot this if I could.
 
  • #3
well it's 1-x all under a square root sign

root(1-x) = sqrt(1-x)

you know?
 
  • #4
okay got it so that's why x>1 or y>1 is out of bounds if you're dealing with real numbers but okay for complex numbers.

so I got a sideways parabola from ending at z=0 x=1 y=1

You might google on graph 3D calculator and try your formula. I did but I didnt have the flash plugin installed (I'm on linux) so I had to imagine how it looks rotating the x curve around (1,1,0)
 
  • #5
really..hmm.. I got a rectangular plane - I don't think we are considering z here? hold it constant, and just focus on y and x right?

so we have x and y have both to be less than or equal to negative one. So they intersect on a rectangular plane going back to negative infinity...?
 
  • #6
Assuming you are just dealing in real numbers, your domain is simply to do with x and y and it is [itex]\{x,y \in\mathbb R: x \leq 1,\ y \leq 1\}[/itex]
 

1. What is the domain of the function f(x,y)=root(1-x)+root(1-y)?

The domain of a function refers to the set of all possible input values for which the function is defined. In this case, the function f(x,y)=root(1-x)+root(1-y) is defined for all real numbers greater than or equal to 0. This means that the domain of the function is x≤1 and y≤1.

2. How do you determine the domain of a function?

To determine the domain of a function, you need to consider any restrictions on the input values that would make the function undefined. This could include values that would result in division by 0, negative inputs for functions that involve square roots, or values that would make the function undefined in other ways. In this case, the function f(x,y)=root(1-x)+root(1-y) has two square roots, so the input values must be non-negative to avoid undefined results.

3. Can the domain of a function be negative numbers?

Yes, the domain of a function can include negative numbers. However, this depends on the specific function and its restrictions. In the case of f(x,y)=root(1-x)+root(1-y), the domain is limited to non-negative numbers because of the square root function. But there are many functions that can have negative numbers in their domain, such as f(x)=x^2.

4. Is the domain of a function always a continuous set of numbers?

No, the domain of a function does not have to be a continuous set of numbers. In some cases, the domain may have gaps or be a discrete set of numbers rather than a continuous range. For example, the function f(x)=1/x has a domain of all real numbers except 0, which creates a gap in the domain.

5. Can the domain of a function change?

Yes, the domain of a function can change depending on the function itself. For example, if we modify the function f(x,y)=root(1-x)+root(1-y) to f(x,y)=root(x)+root(1-y), the domain would change to x≥0 and y≤1. The domain of a function can also be changed by applying transformations such as translations or reflections to the original function.

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