How do I find the domain of #f(x)=2x#?
Since the problem is very simple, I would like not to bother you with theory or definitions, but just try to think about what your problem means.
When people need explanations about functions, I like to tell them to think of functions as some kind of robot, which takes a number as an input, and gives you a number as an output. The problem is that this operation is not always possible. Take, as a simple example, the function
The problem is that you can't give that robot 0 as an input, since he won't be able to give you back
So, the problem with domains is: "which numbers would my robot refuse?" "When the operation I'm trying to do is not allowed?"
In your case, your function takes a number, and doubles it. Is there any number you can't double? Of course not, since the double of a number is well defined for every number.
When there are no restrictions, there are no values to exclude, and thus your domain is given by the whole real number set,