Question

Please help. Which function has the domain x>=-11

Answer 1

we proceed to resolve each case to determine the solution

we know that

The radicand is a number or quantity from which a root is to be extracted

In this problem the radicand must be greater than or equal to zero

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

the radicand is equal to

$(x+11)$

so

$(x+11) \geq 0\\x \geq -11$

the domain is the interval--------> [-11.∞)

therefore

the function  $y=\sqrt{x+11} +5$ is the solution of the problem

case B $y=\sqrt{x-11} +5$

the radicand is equal to

$(x-11)$

so

$(x-11) \geq 0\\x \geq 11$

the domain is the interval--------> [11.∞)

therefore

the function  $y=\sqrt{x-11} +5$ is not the solution of the problem

case C $y=\sqrt{x+5}-11$

the radicand is equal to

$(x+5)$

so

$(x+5) \geq 0\\x \geq -5$

the domain is the interval--------> [-5.∞)

therefore

the function  $y=\sqrt{x+5} -11$ is not the solution of the problem

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

the radicand is equal to

$(x+5)$

so

$(x+5) \geq 0\\x \geq -5$

the domain is the interval--------> [-5.∞)

therefore

the function  $y=\sqrt{x+5}+11$ is not the solution of the problem

the answer is the function $y=\sqrt{x+11} +5$

Answer 2

Answer: Choice A

Set the radicand (stuff under the radical) greater than or equal to 0. Solve x+11 >= 0 for x to get x >= -11