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)#
What is the domain of the function #f(x)=\frac{1}{x+9}#?
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