Question

If g and f(g(x)) are both onto, does it follow that f is onto? If g and f(g(x)) are both onto, does it follow that f is onto? @Mathematics

Answer 1

but why

Answer 2

what if the domain is not g(X)

Answer 3

though there's a different answer here

Answer 4

http://openstudy.com/study#/updates/4ec3ed87e4b030637980032a

Answer 5

There is a theorem where it says if f nd g are both onto then gof is also onto.

Answer 6

gof is g(f(x))

Answer 7

experment i saw that answer from that link but its confusing

Answer 8

yes ..
Looks like i misunderstood the term onto ... I think I am wrong.

Answer 9

ajprincess but does that mean that this theorm proves that if g and fOg are onto then f is also onto

Answer 10

it says that for every element y co-domain there's at least one value of x in domain x.

Answer 11

ya i guess so.

Answer 12

which proves that f is also onto.

Answer 13

@ajprincess i think quite not.

Answer 14

y? @experimentX

Answer 15

=> symbol means implies

f, g are onto => fog is onto => gof is onto
f, gof are onto does not => g is onto

logic does not flow in both way if something happens due to something, thats the way of algebra

Answer 16

yep u r right.

Answer 17

experiment im confused sorry can u give me the last answer and a simple the proof

Answer 18

choose any number 'w'

Answer 19

now if you can find a number 'x' such that 'f' of x is w, then the function is onto.

Answer 20

ok i understand it but dont know how to write it on my hw because he asked to show my work

Answer 21

write this way,
given that g(x) is onto and f(g(x)) is onto

which means, f(g(x)) = w, ie for every 'w', there is y = g(x)
and g(x) = y, there is 'x' for every 'y',



Now it wouldn't be problem if we change, W to Y because f(g(x)) is onto and for every y, there will be x