No, it's not. That would be [itex]x^2- y\ne 0[/itex]. You are requiring that y be less than x2.Derill03 said:define the natural domain and range for f(x,y) = 1/sqrt(x^2-y)
I get D= {(x,y)|x^2-y>0} same as saying y can not equal x^2
And, as Dick said, the range of f is a set of numbers, not of pairs of numbers.R= {(x,Y)|f>0}
can someone tell me if I've approached this correctly?
The domain of a function f(x,y) is the set of all possible input values or independent variables for which the function is defined. It is typically represented as "x" in the function notation f(x,y). The range of a function f(x,y) is the set of all possible output values or dependent variables that result from the input values in the domain. It is typically represented as "y" in the function notation f(x,y).
To find the domain of a function f(x,y), you need to determine all the possible values that x can take without causing the function to be undefined. This can be done by looking at the restrictions on x in the function, such as division by zero or taking the square root of a negative number. To find the range of a function f(x,y), you need to determine all the possible values that y can take by plugging in different values for x in the function and observing the resulting output values.
No, the domain and range can vary for different functions. It depends on the restrictions and conditions of the specific function. For example, a linear function will have a domain and range that includes all real numbers, while a square root function will have a domain that only includes non-negative numbers and a range that only includes non-negative output values.
Yes, the domain and range of a function can be infinite if the function is not restricted by any specific conditions. For example, the domain and range of a linear function are infinite, as it can take on any real number as an input or output value.
The domain and range of a function f(x,y) are closely related to the graph of the function. The domain and range determine the horizontal and vertical values, respectively, that will be included in the graph. The graph of a function can also help identify any restrictions or conditions on the domain and range. For example, if the graph of a function has a vertical asymptote, it indicates that there is a restriction on the domain. Similarly, if the graph has a horizontal asymptote, it indicates a restriction on the range.