How would you notate the Domain restrictions of the following function?

Question

anonymous · Answer

$\ \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 · Answer

@FoolForMath

freckles · Answer

Well first of all when is the bottom 0?

lgbasallote · Answer

@rebeccaskell94  help

freckles · Answer

Then you will look at when x-2>=0
Since you can only have radical of a positive or neutral number

freckles · Answer

But don't forget to exclude when the bottom is 0

anonymous · Answer

@bluepig148

freckles · Answer

This (a,b] means you don't include a but you do include b

freckles · Answer

And it also means you include everything between a and b

freckles · Answer

The bracket things means include the endpoint
The parenthesis things means don't include endpoint

anonymous · Answer

So how do you write the domain restrictions?

freckles · Answer

Well that is why I was asking you when is the bottom 0 and when is x-2>=0

anonymous · Answer

Well, x can not equal 0, and x can not equal 2?

freckles · Answer

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 · Answer

There are other ways to write the domain

freckles · Answer

$$x \in [2,\infty)$$
I used [ instead of ( because I wanted to include 2