Domain

A domain is a set of all inputs over which the function has defined outputs.

Keep following rules in mind when defining the domain :

• Dividing by zero is not allowed!
• It is not possible to take the root of a negative value.

Example

Given is following function $f(x)=\frac1{x}$. Remember, it is not possible to divide a number by zero. For this value the function is not defined. In this case the domain is:

$\mathbb{R} \backslash \{0\}$

or a different notation would be

$\{x\in\mathbb{R}|x\neq0\}$

Notations

We can specify the domain in two different ways:

• Set notation
• Interval notation

Set notation

The previous two notations were examples for the set notation:

• The set of all real numbers $\mathbb{R}$
• The set of real numbers except zero: $\mathbb{R} \backslash \{0\}$
• The set of all real numbers which are not equal to zero: $\{x\in\mathbb{R}|x\neq0\}$

Interval notation

An interval notation is also an option. All numbers in the interval are allowed.

• All numbers between 0 and 3: $[0,3]$
• All numbers between 0 and 3, except 0 (and 3 included): $]0,3]$