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

Mar 26, 2015

#### Explanation:

Use a bracket (sometimes called a square bracket) to indicate that the endpoint is included in the interval, a parenthesis (sometimes called a round bracket) to indicate that it is not.

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

$\left(3 , 7\right)$ 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.
People sometimes say this is $3$ to $7$ "exclusive" (Excluding the endpoints)

$\left[4 , 9\right]$ includes $4$ and every number from $4$ up to $9$, and it also includes $9$
People sometimes say this is $4$ to $9$ "inclusive" (Including the endpoints)

$\left(a , b\right) = \left\{x : a < x \text{ and } x < b\right\}$

$\left[a , b\right] = \left\{x : a \le x \text{ and } x \le b\right\}$

Of course, mixed intervals $\left(a , b\right]$ or $\left[a , b\right)$ are also possible.

The symbols $- \infty$ (and $\infty$) are used to indicate that there is no left (right) endpoint for the interval. They are not endpoints, but indicators that there is no endpoint. They always take parentheses.

Quick examples:

Domain of $f \left(x\right) = \sqrt{x}$ is $\left[0 , \infty\right)$ $\text{ }$ (sqrt0 = 0 is a number.)

Domain of $g \left(x\right) = \frac{1}{\sqrt{x}}$ is $\left(0 , \infty\right)$ $\text{ }$ (1/sqrt0 is a not number.)