### Functions: Domain and range

### Domain

Take a look at the function #f(x)=\sqrt{x}#.

In *roots* we have seen that the root of a negative number does not exist. This means we are not allowed to substitute negative numbers for #x# in the function #f#, since the function does not exist then.

All numbers #x# for which we have #x \geq 0# we can substitue in #f#, these are the numbers in the interval #\ivco{0}{\infty}#.

We say that the **domain** of #f# is equal to the interval #[0,\infty)#.

Domain

The **domain** of a function #f# consists of all arguments of the function.

**Example**

The domain of #f(x)=\sqrt{x-1}# is:

the interval #[1,\infty)#

What is the domain of the function #f(x)=\frac{1}{x-3}#?

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