Answer
$(-8, +\infty)$
Work Step by Step
In order to compute the domain of the given function, we will first exclude those values of $x$ that will make the function undefined or have an imaginary number. The square root function is undefined for negative numbers because the square root of a negative number is an imaginary number.
This means that the value of $x$ can be any real number except those values that will make the denominator equal to zero.
We will equate each factor of the denominator to zero and then simplifying each equation as follows:
$\sqrt {x+8} =0 \\ x+8=0 \\ x=-8$
We observe that the function will have an imaginary number value when the radicand is negative. This shows that the radicand must be greater than or equal to zero.That is,
$x+8 \geq 0 \\ x \geq -8$
Thus, we conclude that the following conditions satisfy the function:
$x \geq -8 $ and $ x \ne 8$.
So, we write the domain of the given function as:
$(-8, +\infty)$
