Recall that the square root is only definied for possitive numbers and zero, therefore, the domain of f(x) consists of all x such that:
[tex]-2x-7\ge0.[/tex]
Adding 7 to the inequality we get:
[tex]-2x\ge7.[/tex]
Dividing by -2 we get:
[tex]x\le-\frac{7}{2}\text{.}[/tex]
Therefore, the domain of f(x) is:
[tex](-\infty,-\frac{7}{2}\rbrack.[/tex]
Answer:
[tex](-\infty,-\frac{7}{2}\rbrack.[/tex]
