Proof that if g o f is Surjective(Onto) then g is Surjective(Onto)

Proof that if g o f is Surjective(Onto) then g is Surjective(Onto). Given two functions f : A to B and g: B to C, we prove that if the composition g o f: A to C is a surjective function then g is also surjective function.

[chirayushah]

OMG I HAVE BEEN STRUGGLING WITH THIS FOR THE PAST WEEK. YOU MADE IT EASY TO UNDERSTAND THANK

[-AnweshaDas-]

YOU ARE INCREDIBLE YOU MADE IT SO EASY THANK

[Absb]

I hate pure math man it is not easy. Respect to all mathematicians

[thebestisyettocome]

You're literally saving my degree

[null.dev.]

Been a good while since I did this at uni.. and after.. a goood while. At first I was like WAIT, just setting b = f(a) has to be proven... then watched again thinking and aha. The video seemed a bit messy to then be fairly concise :) cheers for the refresh. Additionally thankful for Bob Bobson's comment/example from 6 years ago :D.

[robbertcox]

Thanks math sorcerer, big fan of your work🙌

[dhruvmanohar]

bruh i love you saw this in between my test

[chloepozderac]

this is very informative however my problem kind of the reverse


could you PLEASE help with this one? (iA and iB are the identity function on A & B respectively)

Let f A: -> B and g B: -> A be functions such that f o g = iA and g is surjective. Prove
that g o f = iB .

[taeshunho]

What about if g is injective and we need to prove whether or not f is surjective?

[studysike]

Prove that f is onto iff h o f = k o f implies h = k. how to prove this
and if A and B are finite sets with same number of elements then f:A->B is bijective if f is one one and onto?

[BaraNoMatsuri]

Is this true for all A, B, C? Then how about f? Is it surjective for all A, B, C if gof is surjective?

[AU-ywkq]

Ia the converse also true?
If g(x) if surjective then gof(x) is also surjective?

[jk]

so does this mean that f needs to be surjective also?

[krishnageetha]

But f(B)=y isn't an enough condition to be onto right every element is set c should have a preimage in B then I guess we have to take an inverse like some function h(y)=B I am confused pls help

[slimanemesbah]

thanks for the video~ what about f ( is it surjective )

[Itsimane_]

What about f is it surjective or injective ??

[calvinlau]

What if f o g is surjective? Would f be surjective?

[ongkojoyo]

Awww! Thank you so much sir, you made it so easy🙌🏻

[oleksandr]

this is only a one way implication as i am assuming? What would would be a counterexample to the following statement;

if g is surjective, then g o f is surjective

please provide an example when this is not true.

[lisstalikm]

It's still true* upside down? If f is onto, then f ◦ g is onto