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=√(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=√(x+11) +5` is the solution of the problem

case B
`y=√(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=√(x-11) +5` is not the solution of the problem

case C
`y=√(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=√(x+5) -11` is not the solution of the problem

case D
`y=√(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=√(x+5)+11` is not the solution of the problem

the answer is the function
`y=√(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