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Explanations:
The given function is:
f(x) = 2x + 1
By close observation of the function, we can see that x can take on any real numbers as values, that is x∈R. This means that the domain is a set of all real numbers.
The domain of the given function is therefore (−∞,+∞).
Note that the above is an open set.
Since the domain is a set of all real numbers, and the range is gotten by substituting the values of x into the function, the range will also be a set of all real numbers. f(x) ∈ R.
The range is therefore, also (−∞,+∞). Which means that there are no integers or real numbers that do not belong to the range.