The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
Question
The function f(x)=x+1 from the set of integers to itself is onto. Is it True or False?
Solution
The statement is False.
Here's why:
An onto function, also known as a surjective function, is a function where every element in the codomain is mapped to by at least one element in the domain.
The function f(x) = x + 1 is not onto when considering the set of integers.
For example, there is no integer x such that f(x) = 0 because for any integer x, f(x) = x + 1 will always be one more than x, and thus can never be 0.
Therefore, not every integer is mapped to by the function f(x) = x + 1, so the function is not onto.
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