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Are f and g both necessarily onto, if `gof`is onto?

Answer» Let `f: A->B` and `g:B->C` are two functions such that
`gof: A->C`
We are given `gof` is onto.
Let `A = {a_1,a_2,a_3}`
Let `C = {c_1,c_2,c_3}`
As `gof` is onto there will be mapping between each elements of set `C` with every element of set `A`.
Now, Let `B = {b_1,b_2,b_3,b_4}`
As set `B` contains more elements than `A` and `C` so it will not have mapping of its all elements with elements of set `A` and set `C`.
That means it is not neccesary that `f` and `g` are also onto function.


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