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

Question

Paineow · Accepted Answer

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 and x < b}

[a, b] = {x : a \leq x and x \leq b}

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

- \infty, and \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 (x) = \sqrt{x} i s [0, \infty)

,

\sqrt{0} = 0

is a number.
Domain of

g (x) = \frac{1}{\sqrt{x}} i s (0, \infty)

,

\frac{1}{\sqrt{x}}

is a not number.

Ana Robertson · Accepted Answer

I&#039;m really grateful, thanks

user_27qwe · Accepted Answer

When determining the domain or range of a function, it is important to use the appropriate notation to clearly express your answer. In mathematics, we use brackets

[]

and parentheses

()

to represent intervals. The choice between brackets and parentheses depends on whether the endpoints are included or excluded from the interval.
1. Domain:
- Use parentheses

()

when the endpoints are excluded from the interval.
- Use brackets

[]

when the endpoints are included in the interval.
For example, consider the function

f (x) = \frac{1}{x}

:
- To find the domain of

f (x)

, we need to determine the values of

x

for which

f (x)

is defined.
- Since division by zero is undefined, we exclude

x = 0

from the domain.
- Therefore, the domain of

f (x)

is

(- \infty, 0) \cup (0, \infty)

or

(- \infty, 0) \cup (0, \infty)

using parentheses.
2. Range:
- Use parentheses

()

when the endpoints are excluded from the interval.
- Use brackets

[]

when the endpoints are included in the interval.
For example, let's consider the function

g (x) = x^{2}

:
- To find the range of

g (x)

, we need to determine the set of all possible values that

g (x)

can take.
- Since

x^{2}

is always non-negative (or zero), the range of

g (x)

is

[0, \infty)

or

[0, \infty)

using brackets.
In summary, parentheses

()

are used to exclude endpoints, while brackets

[]

are used to include endpoints. It is important to use the appropriate notation to accurately represent the domain or range of a function.

karton · Accepted Answer

The choice between using brackets or parentheses when finding the domain or range depends on whether the endpoints of the interval are included or excluded.
1. Brackets [ ] are used to denote that the endpoint is included in the interval. For example:
- The domain of a function defined on a closed interval [a, b] would be written as

{x \in ℝ : a \leq x \leq b}

.
- The range of a function defined on a closed interval [c, d] would be written as

{y \in ℝ : c \leq y \leq d}

.
2. Parentheses ( ) are used to indicate that the endpoint is excluded from the interval. For example:
- The domain of a function defined on an open interval (a, b) would be written as

{x \in ℝ : a < x < b}

.
- The range of a function defined on an open interval (c, d) would be written as

{y \in ℝ : c < y < d}

.
It's important to consider the context and requirements of the problem to determine whether to use brackets or parentheses.

When should I use brackets or parenthesis in finding domain

Answered question

Answer & Explanation

New Questions in Calculus 1