Answer
No
Work Step by Step
Counter Example:
Suppose that A = {a}
B = {b, c} and
C = {d}
Let g(a) = b,
f(b) = d and
f(c) = d.
Now f and f ◦g
are onto, but g is not onto.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.