Question

what is the domain of $y = \sqrt{x + 7} + 5$? $x \geq 0$; $x \geq -7$; $x \geq 7$; all real numbers

Explanation:

Step1: Recall domain of square root

For a square root function $\sqrt{f(x)}$, the expression inside the square root, $f(x)$, must be non - negative (i.e., $f(x)\geq0$) because the square root of a negative number is not a real number.
In the function $y = \sqrt{x + 7}+5$, the expression inside the square root is $x + 7$. So we set up the inequality $x+7\geq0$.

Step2: Solve the inequality

To solve the inequality $x + 7\geq0$, we subtract 7 from both sides of the inequality.
Subtracting 7 from both sides gives us $x\geq - 7$.

Answer:

$x\geq - 7$ (the option with the text "x ≥ -7")