The domain are the acceptable values that give a real result. 0 is cool. 0=0. That's perfectly fine.
What you do not want are negatives inside the radical. Such as −5+4=−1=i. No good. -5 is NOT in the domain.
Therefore, what is NOT in the domain is (−∞,−4)
Everything from negative infinity up to but not including -4 will result in a negative inside the radical. So, the domain is everything but that.
Domain would be [−4,∞) because those are the parameters that give us real solutions in the range. The bracket means we include -4. A parenthesis would be
everything up to, but not including, 4. See now?.
Since we can have no negative results from a square root, think of it this way: x+4≥0.
Square both sides. Yes, you can do that. x+4≥0
x≥−4. There's the domain. All values of x greater than or equal to -4.
Think of the domain as what goes in and the range as what comes out. The range would be [0,∞)
You seem to think that 0 is not allowed. It is. The domain of x2 would be (−∞,∞) because we can plug in anything in the reals for x and get a real result. 02=0, (−1000)2=1000000 and so on.
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