This maybe dumb but I need help w/ showing work. Determine the intervals where F(x) is continous. Combine multiple intervals with the union symbol.

Question

F(x)= sqrt(x/x^2+15x+56)

I know the answer is easy and it is (-8-7) U [0,infinity)

I get the first part is just factoring it and getting the x's. But how do I show work for getting [0, infinity), the only reason I know it is that is because it is in the answer key and all related questions w different numbers have [0, infinity). How do I show work for this?

Answer 1

Not dumb all! Maybe just not "seeing" something. And that is the square root.

To have real solitons the numerator≥, x ≥ 0.

That is the [0, ∝)