The important thing to remember is that the square root function is defined only for non-negative arguments. In other words, [tex]\sqrt x[/tex] is only defined if [tex]x\ge0[/tex], and thus has domain [tex]x\ge0[/tex].
Some examples:
7. [tex]\sqrt{-x}[/tex] has domain [tex]-x\ge0[/tex], or [tex]x\le0[/tex]
10. [tex]\sqrt{x+7}[/tex] has domain [tex]x+7\ge0[/tex], or [tex]x\ge-7[/tex]
14. [tex]\sqrt{-x-2}[/tex] has domain [tex]-x-2\ge0[/tex], or [tex]x+2\le0[/tex], or [tex]x\le-2[/tex]
