I agree. A comma is typically used as shorthand for "and".mfb said:I guess "x ≠ 0 , y ≠ 0" was meant as "x ≠ 0 or y ≠ 0". The comma is misleading here.
The domain of this function is all real numbers except for when both x and y are equal to zero. This is because the natural logarithm function is undefined when the input is zero, and in this case, both x^2 and y^2 would be equal to zero.
Yes, negative numbers can be part of the domain of this function. The natural logarithm function can accept negative numbers as input, as long as they are not zero. In this case, the function will return a complex number as the output.
No, the domain of this function depends on the values of x and y. As mentioned before, the only restriction is that both x and y cannot be zero. Otherwise, the domain is all real numbers.
Yes, the domain of this function can be extended to include complex numbers. In this case, the function will return a complex number as the output. However, the natural logarithm function is not typically defined for complex numbers, so this extension may not be useful in most cases.
No, there are no other restrictions on the domain of this function. As long as both x and y are not zero, the function will be defined for all real numbers. However, it is important to note that the output of the function may still be limited or undefined for certain input values, such as negative numbers or extremely large numbers.