Question

find the domain of the function.

v (x)=√(x−7)

write your answer as an inequality.
or, you may instead click on \empty set\ or \all reals\ as the answer.

Explanation:

Step1: Recall domain of square root

For a square root function $\sqrt{u}$, the expression inside (radicand) $u$ must be non - negative (i.e., $u\geq0$) to have real - valued output.
In the function $v(x)=\sqrt{x - 7}$, the radicand is $x-7$. So we set up the inequality $x - 7\geq0$.

Step2: Solve the inequality

To solve $x - 7\geq0$, we add 7 to both sides of the inequality.
Adding 7 to both sides gives $x-7 + 7\geq0 + 7$, which simplifies to $x\geq7$.

Answer:

$x\geq7$