Set Builder Notation

roam

Hi!

We have 3 functions; f=, g=[tex]\frac{1}{\sqrt{(2x2 - 1)(x2-1)}}[/tex] and h= [tex]\frac{\sqrt{2+x}+x(x^2-1)}{(x^2-1).\sqrt{2+x}}[/tex]

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 ...

nicksauce

You could write the domain of x as [-2,∞)\{0,±1}
or as
Dom(f) = {x |x [itex]\in[/itex] [-2,∞)\{0,±1}}

Make sense?

Notice the open parentheses on the infinity, since x cannot actually infinity (as it is not a number)

roam

OK, Nick. How should I express the domains of g and h?

Where g = [tex]\frac{1}{\sqrt{(2x^2 - 1)(x^2-1)}}[/tex]

Would the domain of g be written as: dom(g)= R\{0, ±1} ?


And... how would the domain of h be in this notation?

nicksauce

Yes that would be a way to write the domain of g.

For h you could write
Dom(h) = [-2,∞)\{±1}

roam

Right
Thanks a lot! Makes sense now...