Let f(x,y)=(x-1)/(2x+y).
Find the domain of f.
as with all rational functions, the domain is all reals, except where the denominator is zero.
So, you just need to exclude all values in R^2 along the line
2x+y = 0
How did you come to that solution? Could you provide a step by step?
come on. This is just algebra 2.
Division by zero is undefined. So, any values you want can be used to evaluate f(x,y), but you cannot have a denominator of zero.
To find the domain of the function f(x, y) = (x - 1)/(2x + y), we need to determine the set of all possible values for x and y that will not result in undefined expressions.
The function f(x, y) is defined for all values of x and y except when the denominator is equal to zero. Therefore, we need to find the values of x and y that satisfy the equation 2x + y = 0.
Solving this equation for y, we get y = -2x.
Now, examining the equation y = -2x, we can see that there is no restriction on the values of x or y. Therefore, we can conclude that the domain of f(x, y) is all real numbers (x, y) except when 2x + y = 0.