Josh Sizemore

2021-12-13

When should I use brackets or parenthesis in finding domain or range?

Paineow

Beginner2021-12-14Added 30 answers

You should use a bracket (square bracket) to indicate that the endpoint is included in the interval, and a parenthesis (round bracket) to indicate that it is not.

Brackets are like inequalities that say "or equal" and parentheses are like strict inequalities.

For example, (3,7) includes 3.1 and 3.007 and 3.00000000002, but it does not include 3. It also includes numbers greater than 3 and less than 7, but it does not include 7. We can say say this is 3 to 7 "exclusive" (Excluding the endpoints)

[4,9] includes 4 and every number from 4 up to 9, and it also includes 9. We can say this is 4 to 9 "inclusive" (Including the endpoints)

$(a,b)=\{x:a<x{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}x<b\}$

$[a,b]=\{x:a\le x{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}x\le b\}$

Of course, there can be also mixed intervals (a,b] or [a,b).

The symbols$-\mathrm{\infty},\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\infty}$ are used to indicate that there is no left or right endpoint for the interval. They always take parentheses.

For example:

Domain of$f\left(x\right)=\sqrt{x}\text{}is\text{}[0,\mathrm{\infty})$ , $\sqrt{0}=0$ is a number.

Domain of$g\left(x\right)=\frac{1}{\sqrt{x}}\text{}is\text{}(0,\mathrm{\infty})$ , $\frac{1}{\sqrt{x}}$ is a not number.

Brackets are like inequalities that say "or equal" and parentheses are like strict inequalities.

For example, (3,7) includes 3.1 and 3.007 and 3.00000000002, but it does not include 3. It also includes numbers greater than 3 and less than 7, but it does not include 7. We can say say this is 3 to 7 "exclusive" (Excluding the endpoints)

[4,9] includes 4 and every number from 4 up to 9, and it also includes 9. We can say this is 4 to 9 "inclusive" (Including the endpoints)

Of course, there can be also mixed intervals (a,b] or [a,b).

The symbols

For example:

Domain of

Domain of

Ana Robertson

Beginner2021-12-15Added 26 answers

I'm really grateful, thanks

user_27qwe

Skilled2023-06-14Added 375 answers

karton

Expert2023-06-14Added 613 answers

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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