Let A,B and C be sets and let f: A->B and g: B->c be functions. the composite function denoted by g "o" f is a function from A to C defined by
g "o" f(x)= g(f(x)) for every x in A. Prove that if g "o" f is one to one, the f is one to one. Then prove that if g "o" f is onto, then g onto...
Yes, it's the composite function. And no, it's a contradiction because assuming that is non-injective implies that is non-injective.
For the other case it may be easier to approach it this way.
Let then there exists some such that (since is surjective)...but ...so