Domain

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 substitute 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)#

Limited dom‍ain

In this course we will usually look at the biggest possible domain of a function. But it is also possible to limit the domain. For example, with a function that describes the height of a soccer ball after kicking it at time #t=0#, it makes sense to limit the domain of the function to #t\geq 0#.

What is the domain of the function #f(x)=\frac{1}{x+5}#?

All numbers

All numbers greater than #-5#

All numbers except # 5 #

All numbers greater than # 5 #

All numbers less than #-5#

All numbers except #-5#