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Study23
How would you notate the Domain restrictions of the following function?
\(\ \huge f(x)=\frac{\sqrt{x-2}}{x} \). D: ?. Also, what is the difference between the \(\ \huge [ \) and the \(\ \huge ( \) sign when writing the restrictions?
Well first of all when is the bottom 0?
@rebeccaskell94 help
Then you will look at when x-2>=0 Since you can only have radical of a positive or neutral number
But don't forget to exclude when the bottom is 0
This (a,b] means you don't include a but you do include b
And it also means you include everything between a and b
The bracket things means include the endpoint The parenthesis things means don't include endpoint
So how do you write the domain restrictions?
Well that is why I was asking you when is the bottom 0 and when is x-2>=0
Well, x can not equal 0, and x can not equal 2?
Well x can be 2 or greater than 2 since x-2>=0 implies x>=2 \[Domain=\{x \in \mathbb{R} | x \ge 2 \}\]
There are other ways to write the domain
\[x \in [2,\infty)\] I used [ instead of ( because I wanted to include 2