which function has the domain x≥ - 11?\no y = √(x + 11)+5\no y = √(x - 11)+5\no y = √(x + 5)-11\no y = √(x +…

Explanation:

Step1: Recall domain - rule for square - root

For the square - root function $y = \sqrt{u}$, the expression inside the square - root $u\geq0$.

Step2: Check each option

Option 1: $y=\sqrt{x + 11}+5$

Set $u=x + 11$. We want $u\geq0$, so $x+11\geq0$. Solving for $x$ gives $x\geq - 11$.

Option 2: $y=\sqrt{x - 11}+5$

Set $u=x - 11$. We want $u\geq0$, so $x-11\geq0$, which gives $x\geq11$.

Option 3: $y=\sqrt{x + 5}-11$

Set $u=x + 5$. We want $u\geq0$, so $x+5\geq0$, which gives $x\geq - 5$.

Option 4: $y=\sqrt{x + 5}+11$

Set $u=x + 5$. We want $u\geq0$, so $x+5\geq0$, which gives $x\geq - 5$.

Answer:

$y=\sqrt{x + 11}+5$