Question 1194121
.
<pre>

The domain of this function is the set of all real  numbers x, where the expression under the square root is not negative

    x^2 + 10x + 24 >= 0.


Factor left side

    (x+6)*(x+4) >= 0.


The roots are  -6 and -4.


Quadratic function x^2 + 10x + 24 is non-negative on the set

    (-oo,-6] U [-4,oo).


<U>ANSWER</U>.  The domain of the given function is the set of real numbers  (-oo,-6] U [-4,oo).
</pre>

Solved.