How do you know when to use brackets or parentheses in finding domain or range?

Hint: We first describe the difference between the brackets and parentheses. The main difference being the inclusion and exclusion of the endpoints. We understand the concept with an example.

Complete answer:
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket $\left[ {} \right]$ when the set includes the endpoint and a parenthesis \[\left( {} \right)\] to indicate that the endpoint is either not included or the interval is unbounded.
Bracket refers to the equality to the point and parenthesis refers to the strict inequalities.
We take an arbitrary value a. if $a\in \left( x,y \right)$ then it means $x < a < y$ and if $a\in \left[ x,y \right]$ then it means $x\le a\le y$.
In brackets the value of a can be equal to the endpoints or the boundary values but in parenthesis the value of a can’t be equal to the endpoints or the boundary values.
In real number cases we can say that $4\notin \left( 4,5 \right)$ but $4\in \left[ 4,5 \right]$. Same thing can be said about the number 5.

Note:
The use of the brackets and parentheses also describes the inclusiveness and exclusiveness. There are two more combined ways to express the inclusion and exclusion of endpoints. These are $\left[ {} \right),\left( {} \right]$. These are mixed forms.