The explanation of the domain of two variable function

• sayed5555
In summary, the domain of a single variable function is the set of all values for which the function is defined. This can be explicitly stated in the definition of the function, or it can be determined by the natural domain of the formula used to define the function. For functions defined by a formula, the domain is all values for which the formula can be calculated. However, for functions with restrictions, such as dividing by 0 or taking the square root of a negative number, the domain is limited to certain values. It is important to understand the domain in order to correctly evaluate and graph functions.
sayed5555
can anyone explain that domain or give me any reference about it??

Do you know what the domain of a single variable function is? There really isn't any great difference!

The "domain" of a function, of any number of variables, is the set of all values of those variables for which the function is defined. Sometimes that is given as part of the definition of the function. For example, I can define "$f(x,y)= x^2- y^3$ for all positive x and y[/itex]". In that case, the domain is exactly as stated: all positive x and y: the first quadrant of R2; $\{(x, y)|x> 0, y> 0\}$.

Often, a function is "defined" simply by a formula, in which case the domain is the "natural domain", all values of the variables for which the formula can be calculated. If I just said, "$f(x,y)= x^2- y^3$" since we can square, cube, and subtract all numbers, there is no restriction- its natural domain is all of R2: all pairs (x, y).

But if I define $f(x,y)= 1/(x+ y)$, I cannot divide by 0 so x+ y cannot equal 0. That means that y cannot equal -x: The domain is all (x, y) such that $y\ne -x$, all of R2 except the line y= -x.

Similarly, if I define $f(x,y)= \sqrt{x+ y}$, now I cannot take the square root of a negative number so x+ y cannot be negative. The domain is all (x, y) such that $x+y\ge 0$. That would be all of the points in R2 on or above and to the right of the line y= -x.

thank you indeed
i would be grateful if you draw it or give me simples in papers

1. What is the domain of a two variable function?

The domain of a two variable function is the set of all possible input values for the independent variables. In other words, it is the set of all values that can be plugged into the function to produce a valid output.

2. How is the domain of a two variable function determined?

The domain of a two variable function is typically determined by looking at the restrictions or limitations of the independent variables in the function. This can include restrictions based on real-world constraints or mathematical principles.

3. Can the domain of a two variable function be infinite?

Yes, the domain of a two variable function can be infinite if there are no restrictions or limitations on the independent variables. This means that there are an infinite number of possible input values that can be used in the function.

4. Can the domain of a two variable function include negative numbers?

Yes, the domain of a two variable function can include negative numbers as long as there are no restrictions or limitations on the independent variables that would exclude them. This will depend on the specific function and its purpose.

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

The domain of a two variable function can have a significant impact on its graph. It determines the range of values that will be plotted on the x-axis and can also affect the shape and behavior of the graph. If the domain is limited, the graph may have gaps or breaks, while an infinite domain can result in a continuous graph.

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