How do I find the domain of #f(x)=2x#?

Answer 1

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 #\frac{1}{x}#. What does this "robot" do? You give him a number, and he gives you back 1 divided by that number. You give him 1, he gives you 1; you give him 2, he gives you #1/2#, and so on.
The problem is that you can't give that robot 0 as an input, since he won't be able to give you back #\frac{1}{0}# as an output.

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, #\mathbb{R}#.
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Answer 2

The domain of ( f(x) = 2x ) is all real numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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