Give examples of two functions f: N → N and g: N → N such that gof is onto, but f is not onto.

Question

Philoid · Accepted Answer

Define f:N → N by, f(x) = x + 1 And, g: N → N by,

We first show that f is not onto.

For this, consider element 1 in co – domain N. It is clear that this element is not an image of any of the elements in domain N.

Therefore, f is not onto.