# If f:X→Y is onto and g:Y→Z is onto,then prove that gof:X→Z is onto.

jitender lakhanpal
62 Points
12 years ago

Dear Menka,

in order to prove that gof:X→Z is onto we have to show that every element in Z

has it's pre image in X i.e

if  C be an arbitrary element of Z,B be an arbitrary element of Y, A be an arbitrary element of Z.

for all C belongs to Z there exists A belongs X such that (gof)(A)=C ------------to prove

as        f:X→Y is onto that means  f (A) = B-------------------1

g:Y→Z is onto that means  g (B) = C        ----------------------2

 from 1 & 2   we get
 gof(A) = g(f(A))=g(B) = C
hence proved

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jitender

Aman Bansal
592 Points
12 years ago

Dear Menka,

Assume an element x1 since x,y and y,z are onto we can prove that x,z is also onto.

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Thanks

Aman Bansal

290 Points
12 years ago

Hi Menka,

The solution is written in the scanned copy.

Hope that helps.

All the best,

Regards,