SOLUTION: determine the domain and range of the function y=√x^2+10x+24

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Question 1194121: determine the domain and range of the function y=√x^2+10x+24
Answer by ikleyn(52781) About Me  (Show Source):
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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).


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

Solved.