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