SOLUTION:
[tex]F(x,y)=\sqrt{y+3x}[/tex]We want to determine the domain of the function of two variables, The function is defined for those values of x,y for which the square root is defined;
[tex]\begin{gathered} y+3x\ge0 \\ y\ge-3x \end{gathered}[/tex]Thus, the domain of the function is ;
[tex]\lbrace(x,y):y+3x\ge0\rbrace[/tex]