What Values of (x, y) Make f(x, y) = 1/(x - y^2) Undefined?

Thread starter M.Qayyum
Start date Aug 23, 2009
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Domain

In summary, the domain of a function with two variables is the set of all possible values for the independent variables. To determine the domain, you need to consider any restrictions on x and y that would result in undefined or imaginary outputs. The domain can be infinite, depending on the nature of the function. The range, on the other hand, refers to the set of all possible outputs. The domain can change depending on the context and restrictions of the function.

Aug 23, 2009

M.Qayyum

Here is my question, that what is the domain of f, while
f(x,y)=1/(x-y²)

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Aug 23, 2009

MechanicalMan

Ask yourself this question, and you'll have answered your own question:

For what values of (x,y) is f(x,y) undefined?

Related to What Values of (x, y) Make f(x, y) = 1/(x - y^2) Undefined?

1. What is the domain of f(x,y)?

The domain of f(x,y) is the set of all possible values that the independent variables, x and y, can take on in a given function. It represents the input values for the function.

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

To determine the domain of a function with two variables, you need to consider the restrictions on both variables. Look for any values of x and y that would result in undefined or imaginary outputs. The domain will be all the possible values of x and y that do not violate these restrictions.

3. Can the domain of f(x,y) be infinite?

Yes, the domain of a function with two variables can be infinite. It depends on the nature of the function and the range of values that x and y can take on. For example, if the function is a polynomial, the domain will be all real numbers, which is infinite.

4. What is the difference between the domain and the range of a function?

The domain of a function refers to the input values, while the range refers to the output values. In other words, the domain is the set of all possible x and y values, while the range is the set of all possible f(x,y) values.

5. Can the domain of a function change?

Yes, the domain of a function can change depending on the context and restrictions. For example, if a function includes a square root, the domain will be limited to non-negative values. If the function is a rational expression, the domain will be all real numbers except for the values that make the denominator equal to 0.