1. The problem statement, all variables and given/known data If f and g are both onto show g°f is onto. f:X→Y and g:Y→Z 2. Relevant equations 3. The attempt at a solution Since f is onto then there exists an x in X such that f(x) = y, for all y in Y. Since g is onto then there exists a y in Y such that g(y) =z for all z in Z. Hence, if g°f is not onto then there exists a z in Z such that there is no corresponding x in X. But since g and f are onto this is not possible. Therefore, g°f is onto.