Q. 144.0( 3 Votes )

If f: A B and g: B C are onto functions show that gof is an onto function.

Answer :

We have, f: A B and g: B C are onto functions.


Now, we need to prove: gof: A C is onto.


let y C, then


gof (x) = y


g(f(x)) = y ……(i)


Since g is onto, for each element in C, there exists a preimage in B.


g(x)=y ……(ii)


From (i) & (ii)


f(x)=x


Since f is onto, for each element in B there exists a preim age in el


f(x)=x ……(iii)


From (ii)and(iii) we can conclude that for each y C, there exists a preimage in A such that gof(x) = y


gof is onto.


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