Set Builder Notation: Domain of f, g & h

[roam]

Hi!

We have 3 functions; f=http://img59.imageshack.us/img59/8682/fovgdt3.png ,[/URL] 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 ...

 

[nicksauce]

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)

 

[roam]

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?

 

[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...