Question

Which function has the domain x>-11

Answer 1

Answer

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

Explanation

Remember that the square root function is not defined, in the set of real numbers, for negatives values, so its radicand (the thing inside the square root) must be zero or bigger than zero. In other words, to find the domain of a square root function, you should set the thing inside the radical bigger or equal to zero and solve for x. Let's find the domain of each one of our functions:

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

The thing inside the square root is $x+11$, so we are setting that bigger or equal than zero and solve for x to find the domain of the function:

$x+11\geq 0$

$x\geq -11$   domain

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

$x-11\geq 0$

$x\geq 11$   domain

For $y=\sqrt{x-5} -11$ and $y=\sqrt{x-5} +11$

$x+5\geq 0$

$x\geq -5$   domain

As you can see, the only one that has the domain $x\geq -11$ is the first choice.