Domain sketch for multiple variables function

How do I sketch the domain of the function f(x,y) =\dfrac{sqrt(y-x^2)}{(1-x^2)}

How to sketch domain D f(x,y)<=0 on Oxy?

This is for my exercise so I really need some help. Thanks in advanced!

Answer 1

[Mathy]

Hi Khoa,

You can make use of the example below to sketch the domain of the provided function:

% Define the range for x and y
x = linspace(-1, 1, 100); % 100 points between -1 and 1
y = linspace(4, 8, 100);  % 100 points between 4 and 8

% Create a meshgrid of x and y values
[X, Y] = meshgrid(x, y);

% Calculate the function values
Z = sqrt(Y - X.^2) ./ (1 - X.^2);

% Handle the points where the function is undefined (x = 1 or x = -1)
Z(abs(X) == 1) = NaN;

% Plot the function
surf(X, Y, Z);
xlabel('x');
ylabel('y');
zlabel('f(x, y)');
title('Plot of f(x, y) = sqrt(y - x^2) / (1 - x^2)');

The resulting sketch would look something like this:

Hope this helps!

[Hassan]

Z=sqrt(x^2-2y)