## Study23 3 years ago How would you notate the Domain restrictions of the following function?

1. Study23

$$\ \huge f(x)=\frac{\sqrt{x-2}}{x}$$. D: ?. Also, what is the difference between the $$\ \huge [$$ and the $$\ \huge ($$ sign when writing the restrictions?

2. Study23

@FoolForMath

3. freckles

Well first of all when is the bottom 0?

4. lgbasallote

5. freckles

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

6. freckles

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

7. Study23

@bluepig148

8. freckles

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

9. freckles

And it also means you include everything between a and b

10. freckles

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

11. Study23

So how do you write the domain restrictions?

12. freckles

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

13. Study23

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

14. freckles

Well x can be 2 or greater than 2 since x-2>=0 implies x>=2 $Domain=\{x \in \mathbb{R} | x \ge 2 \}$

15. freckles

There are other ways to write the domain

16. freckles

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