Declaring the domain of a function of two variables.

In summary, the domain of a function of two variables is the set of all possible input values for the variables in the function. To declare the domain, restrictions on the input values must be determined. It is important to declare the domain to ensure the function is well-defined and avoid errors. Common domains include all real numbers, positive or negative real numbers, positive integers, and specific ranges. The domain can affect the graph by limiting the range of values and causing gaps or discontinuities.
  • #1
lo2
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Homework Statement



I have this function of two variables:

[itex]f(x,y)=\sqrt{4xy-3y^2}[/itex]

Where I have to declare the domain of the function.

Homework Equations



Since you cannot take the square root of something negative, when dealing with real numbers. The square root has to be zero or above.

The Attempt at a Solution



Well I just wanted to know if this is a sufficient answer:

[itex]D_f = \{(x,y) = 4xy-3y^2 \geq 0 \}[/itex]
 
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  • #2
Yes, it is. That is the "natural domain" of the given function.
 

FAQ: Declaring the domain of a function of two variables.

What is the domain of a function of two variables?

The domain of a function of two variables is the set of all possible input values for the variables in the function. It represents the range of values that the independent variables can take on in order for the function to be defined.

2. How do you declare the domain of a function of two variables?

To declare the domain of a function of two variables, you need to determine the restrictions or limitations on the values that the independent variables can take on. This can be done by looking at the given equation or by considering the context of the problem.

3. Why is it important to declare the domain of a function of two variables?

Declaring the domain of a function of two variables is important because it helps to ensure that the function is well-defined and meaningful. It also helps to avoid any potential errors or inconsistencies in the results obtained from the function.

4. What are some common domains for functions of two variables?

Some common domains for functions of two variables include all real numbers, positive or negative real numbers, positive integers, and specific ranges of numbers such as 0 to 100 or -10 to 10.

5. How does the domain of a function of two variables affect its graph?

The domain of a function of two variables can affect its graph by limiting the range of values that can be plotted on the x and y axes. It can also result in gaps or discontinuities in the graph if there are any restrictions or limitations on the input values.

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