Quote Originally Posted by TheMathsDude View Post
Finding it hard to manipulate the surjective definition to fit the previous examples written.

Any clues?
i'll help you out, i leave the actual proof to you, but i'll give you somewhat of an outline.

Definition: A function f is surjective (or onto) if for every y in the codomain of f, there is an x in the domain of f such that f(x) = y

now what that basically means, is that the range of the function is the same as the codomain of the function.

so we have f : A \to B and g:B \to C. so g \circ f : A \to C.

so, since g \circ f is surjective, C is the codomain and at the same time, the range of g \circ f. now what g \circ f does, is use the function f to take some element x \in A and put it in B and then use the function g to take that element and then move it to C. this last part of the function is what makes it surjective, since it is the part that maps x to the range (which is the codomain).