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# Core 3

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1. So in the domain and range questions when do i use the ( brackets and [ brackets?
P.16
2. (Original post by Ayaz789)
So in the domain and range questions when do i use the ( brackets and [ brackets?
P.16
Generally square brackets are used when inclusive of a value and parentheses if excluding that value.

i.e. [1,2) is an interval that includes 1 but not 2.
3. (Original post by Alexion)
Generally square brackets are used when inclusive of a value and parentheses if excluding that value.

i.e. [1,2) is an interval that includes 1 but not 2.
Im sorry but i don't understand
4. For example this in the markscheme:

is the range of values in between 1 and 1.5 that includes 1.5 but does not include 1.
5. (Original post by Alexion)
For example this in the markscheme:

is the range of values in between 1 and 1.5 that includes 1.5 but does not include 1.
But how do you know if it includes that number or not? And do you get deducted marks if you get them wrong?
6. (Original post by Ayaz789)
But how do you know if it includes that number or not? And do you get deducted marks if you get them wrong?
It depends how you're working out the range/domain ~ whether it can take that value or not.

~ If it's asymptotic at a value, then the range won't include that value, so you use a parenthesis.
~ If it's a numerical maximum/minimum, it can take that value, so you'd use a square bracket.

I don't think they penalise for it, but better safe than sorry
7. (Original post by Alexion)
It depends how you're working out the range/domain ~ whether it can take that value or not.

~ If it's asymptotic at a value, then the range won't include that value, so you use a parenthesis.
~ If it's a numerical maximum/minimum, it can take that value, so you'd use a square bracket.

I don't think they penalise for it, but better safe than sorry
I should get 100 Ums hopefully if they don't penalise me for this but like i get mixed up with squares and curved brackets , so the way i see it is if you have like a value that doesn't have a proper value like infinity it will have a curved bracket or like if you put infinity in the bracket to get the range then it'll be curved bracket ygm?
Thankss anyways, much appreciated mathematician!
8. (Original post by Ayaz789)
I should get 100 Ums hopefully if they don't penalise me for this but like i get mixed up with squares and curved brackets , so the way i see it is if you have like a value that doesn't have a proper value like infinity it will have a curved bracket or like if you put infinity in the bracket to get the range then it'll be curved bracket ygm?
Thankss anyways, much appreciated mathematician!
That's because isn't a real number.
9. (Original post by Zacken)
That's because isn't a real number.
Yeah ik but like where else can i use a curved bracket , i really don't understand where to use them :L
10. (Original post by Ayaz789)
Yeah ik but like where else can i use a curved bracket , i really don't understand where to use them :L
Whenever you need to specify a non-inclusive interval.
11. (Original post by Zacken)
Whenever you need to specify a non-inclusive interval.
Like what do you mean by that?
12. (Original post by Ayaz789)
Like what do you mean by that?
Like if I told you to write down the set of numbers between 1 and 2 that don't include the number 1 or 2.
13. (Original post by Zacken)
Like if I told you to write down the set of numbers between 1 and 2 that don't include the number 1 or 2.
If you told me to write a set of numbers between 1 and 2 that dont include 1 and 2 huh? Ill tell you an example to do , 1 min
14. (Original post by Ayaz789)
Like what do you mean by that?
[a,b] means all the real numbers between a and b including a and b.
(a,b) means all the real numbers between a and b excluding a and b.
[a,b) means all the real numbers between a and b including a and excluding b.
(a,b] means all the real numbers between a and b excluding a and including b.
Of course, if a or b are ±infinity, then there will be a round bracket because obviously infinity is not included.

That's about as comprehensive of an explanation you can get.
15. (Original post by Ayaz789)
If you told me to write a set of numbers between 1 and 2 that dont include 1 and 2 huh? Ill tell you an example to do , 1 min
What?
16. (Original post by Zacken)
What?
9aii? Why is the -16 in a round bracket?
17. (Original post by Ayaz789)
9aii? Why is the -16 in a round bracket?
Because the range of fg does not include -16. To see why, complete the square or find the minimum however you want.
18. (Original post by Zacken)
Because the range of fg does not include -16.
But how do you know it doesnt include it? Where does it say that?
19. (Original post by Ayaz789)
But how do you know it doesnt include it? Where does it say that?
20. (Original post by Zacken)
Complete the square on what? On fg(x)?

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