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Set Builder Notation

by roam
Tags: builder, notation
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roam
#1
Jul30-08, 05:37 PM
P: 895
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 ...

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nicksauce
#2
Jul30-08, 06:22 PM
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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
#3
Jul30-08, 07:01 PM
P: 895
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
#4
Jul30-08, 07:57 PM
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Set Builder Notation

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

For h you could write
Dom(h) = [-2,∞)\{1}
roam
#5
Jul30-08, 08:09 PM
P: 895
Right
Thanks a lot! Makes sense now...


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