anonymous
  • anonymous
How would you notate the Domain restrictions of the following function?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\(\ \huge f(x)=\frac{\sqrt{x-2}}{x} \). D: ?. Also, what is the difference between the \(\ \huge [ \) and the \(\ \huge ( \) sign when writing the restrictions?
anonymous
  • anonymous
freckles
  • freckles
Well first of all when is the bottom 0?

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lgbasallote
  • lgbasallote
freckles
  • freckles
Then you will look at when x-2>=0 Since you can only have radical of a positive or neutral number
freckles
  • freckles
But don't forget to exclude when the bottom is 0
anonymous
  • anonymous
freckles
  • freckles
This (a,b] means you don't include a but you do include b
freckles
  • freckles
And it also means you include everything between a and b
freckles
  • freckles
The bracket things means include the endpoint The parenthesis things means don't include endpoint
anonymous
  • anonymous
So how do you write the domain restrictions?
freckles
  • freckles
Well that is why I was asking you when is the bottom 0 and when is x-2>=0
anonymous
  • anonymous
Well, x can not equal 0, and x can not equal 2?
freckles
  • freckles
Well x can be 2 or greater than 2 since x-2>=0 implies x>=2 \[Domain=\{x \in \mathbb{R} | x \ge 2 \}\]
freckles
  • freckles
There are other ways to write the domain
freckles
  • freckles
\[x \in [2,\infty)\] I used [ instead of ( because I wanted to include 2

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