# Set Builder Notation

by roam
Tags: builder, notation
 P: 916 Hi! We have 3 functions; f=, g=$$\frac{1}{\sqrt{(2x2 - 1)(x2-1)}}$$ and h= $$\frac{\sqrt{2+x}+x(x^2-1)}{(x^2-1).\sqrt{2+x}}$$ And we want to write the domain of these functions in the set builder notation, which I'm not very familiar with. Well, I know that for the Domain of g, x ≠ 0 and ±1. How do we write it in that notation? is it [0,∞]\{±1}? For the domain of f, x must be greater than or equal to -2 and it cannot equal 0 & ±1 In h, domain: x≥-2, & it can't be ±1 as well. I need to write the domains of these functions in the set builder notation. Not knowing something doesn't mean you're stupid, just asking about it ...
 Sci Advisor HW Helper P: 1,275 You could write the domain of x as [-2,∞)\{0,±1} or as Dom(f) = {x |x $\in$ [-2,∞)\{0,±1}} Make sense? Notice the open parentheses on the infinity, since x cannot actually infinity (as it is not a number)
 P: 916 OK, Nick. How should I express the domains of g and h? Where g = $$\frac{1}{\sqrt{(2x^2 - 1)(x^2-1)}}$$ Would the domain of g be written as: dom(g)= R\{0, ±1} ? And... how would the domain of h be in this notation?