Question

how do you find the domain of sqrt(x+4)-2?

Answer 1

Well, lets think to the left first.
When x=-4 we have
\[\sqrt{-4+4}-2=\sqrt 0 -2 = -2\]
but when we go to x=-5
\[\sqrt{-5+4}-2=\sqrt{-1}-2=-2+i\]
So, it isnt defined by the reals starting at x=-5, but actually thats true at x=-4.00001
Now we know, x=-4 is the furthest left we can go. Getting bigger, we dont have any threat of going undefined
\[\sqrt{10^{100}-2}-2\]
exists, so our domain must be
\[-4\le x\le\infty\]

Answer 2

I see now, I was missing an easy piece. Thank you!

Answer 3

no problem.