find the domain of the function f (x,y) = e^-xy

The domain of any exponential is all real numbers. Just think of the graph; it extends across the whole real line.

To find the domain of the function f(x, y) = e^(-xy), we need to determine for which values of x and y the function is defined.

The exponential function e^(-xy) is defined for all real values of x and y, which means there are no restrictions on the domain of this function.

Therefore, the domain of f(x, y) = e^(-xy) is the set of all real numbers for both x and y.

To find the domain of the function f(x, y) = e^(-xy), we need to determine the set of all possible values for x and y for which the function is defined.

The function f(x, y) = e^(-xy) involves the operation of taking the exponential of a number, which is defined for all real numbers. Therefore, there are no restrictions on the values of x and y with respect to the exponential part of the function.

However, it's important to note that the domain of the function may be limited by other factors, such as the possibility of division by zero or taking the square root of a negative number. In this case, since there are no such factors in the function f(x, y) = e^(-xy), the domain is unrestricted.

So, the domain of the function f(x, y) = e^(-xy) is the set of all real numbers for both x and y.