Answer :
Final answer:
The function f(x) = 2x + 1 is both a one-to-one and an onto function because each input has a unique output, and every possible output has a corresponding input.
Explanation:
The given function is f(x) = 2x + 1, where x is a real number. To answer the question, we evaluate the nature of this function.
- It is a function because for each input x, there is exactly one output f(x).
- It is a one-to-one function because each output value is the result of exactly one input. This is due to the fact that the function has a slope of 2, which means for each unit increase in x, f(x) increases by 2, ensuring that no two different x values map to the same f(x) value.
- It is an onto function (or surjective) on the real numbers because for every real number you could choose as an output, there's an x that when plugged into the function will produce that output.
Therefore, the correct answer is E. This is a one-to-one and onto function.
