Question 261190
{{{f(x) = sqrt(x+2)}}}
The domain of the function is the set of allowable values for x. There are several reasons for disallowing values for x:<ul><li>Denominators must not be zero!!</li><li>Radicands (the expression in an radical) of even-numbered roots must never be negative (for Real-valued functions).</li><li>Arguments to logarithms must never be zero or negative. (IOW, they must be positive.)</li><li>Other undefined expressions like {{{tan(pi/2)}}}</li></ul>
The only one of these your function has is an even-numbered root. (Square roots are 2nd roots.) So the only thing we have to avoid is a negative value for the radicand. Put another way, our domain must ensure that the radicand, x+2, is equal to zero or positive. In Math terms, the domain is the solution to:
{{{x + 2 >= 0}}}
Solve this and you have your domain.