The correct option is C h is onto ⇒ g is onto
Given, h=g(f(x))=g.f
Consider the following arrow diagram
From above diagram it is clear that
g is not onto ⇒h=g.f is also not onto, since the co-domain of g is same as the co-domain of g.f.
The contrapositive version of the above implication is
h is onto ⇒g is onto
which also has to be true since direct ≡ contrapositive.
So option (c) is true.