Set Builder Notation: Domain of f, g & h

In summary, the conversation discussed writing the domain of three functions (f, g, and h) in set builder notation. It was mentioned that for the domain of g, x cannot equal 0 or ±1, and for f and h, x must be greater than or equal to -2 and cannot equal 0 or ±1. The suggested notations for the domains were Dom(f) = {x |x \in [-2,∞)\{0,±1}}, Dom(g) = R\{0, ±1}, and Dom(h) = [-2,∞)\{±1}.
  • #1
roam
1,271
12
Hi!

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

 
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  • #2
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)
 
  • #3
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?
 
Last edited:
  • #4
Yes that would be a way to write the domain of g.

For h you could write
Dom(h) = [-2,∞)\{±1}
 
  • #5
Right :wink:
Thanks a lot! Makes sense now...
 

What is Set Builder Notation?

Set Builder Notation is a mathematical notation used to describe the elements of a set using a rule or condition. It is written in the form {x | x satisfies the rule or condition}.

How is Set Builder Notation used to represent the domain of a function?

The domain of a function represents all the possible input values that the function can take. In Set Builder Notation, the domain of a function is written as {x | x is a valid input for the function}.

What does the notation f(x) mean?

The notation f(x) represents the output of a function f when given an input value x. It is read as "f of x".

How do you determine the domain of a composite function using Set Builder Notation?

A composite function is a combination of two or more functions. To determine the domain of a composite function, we need to find the common domain of all the individual functions involved. This can be represented in Set Builder Notation as {x | x is a valid input for all the functions in the composite function}.

Can Set Builder Notation be used to describe the domain of a relation?

Yes, Set Builder Notation can be used to describe the domain of any relation, not just functions. In this case, the notation would be {x | x is a valid input for the relation}.

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