Question

A function f is onto if ∀y∃x(f (x) = y), where the domain for x is the domain of the function and the domain for y is the codomain of the function.

true or false

Answer 1

A function f is onto if every element in the codomain is paired with at least one element from the domain.

Step-by-step explanation:

The statement given, "A function f is onto if ∀y∃x(f (x) = y), where the domain for x is the domain of the function and the domain for y is the codomain of the function" is true.

In simpler terms, a function f is onto if every element in the codomain is paired with at least one element from the domain.

For example, if we have a function f(x) = x^2, the domain could be all real numbers, and the codomain could also be all real numbers. In this case, the function is onto because for every real number y, we can find at least one real number x (both positive and negative) such that f(x) = y.