Question

A function f is onto if and only if, each element in the codomain of f is the image of at _____ one element in the domain of f

Answer 1

A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.

Explanation:

A function f is onto if and only if, each element in the codomain of f is the image of at least one element in the domain of f.

Let us consider a function f which maps the elements of X to each element in the domain of f, such that

f(1) = D

f(2) = B

f(3) = C

f(4) = C

From here, we can determine the domain and range, so

Domain X of f = {1, 2, 3, 4}

Domain Y of f = {D, B, C}

Therefore, it is clear that every element in the codomain of f is the image of at least one element in the domain of f.