Math Functions Domain

# Domain

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

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### Remember

The domain contains all values which are accepted as the input of a function.

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

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

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### Hint

Both notations mean the same.

$\mathbb{R}$ stands for the real numbers. In other words, those are all the numbers that you know.

## 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): $]0,3]$
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### Info

Closed square brackets mean that the number is included in the interval. Open square brackets mean that the number itself is not included in the interval anymore.