/sci/ - Science & Math

PLEASE HELP ME
a) Consider the following functions:
>pic related
>mit = with
Specify fi for each of the above functions. if it's injective and if it's surjective. For each non-injective function fi, enter two elements x, y ∈ Def(fi), so that x 6 ≠ y and fi(x) = fi(y) applies. For each non-surjective function fi, specify an element x from the image area, so that x ∉ picture (fi) applies. You do not need to justify your answers.

b) Be A, B and C any quantities and f : A B and g : B C any functions. We define the function h: A C as the concatenation of f and g through.

h(a):= g(f(a)) a)) f.a, a ∈ A

I) Show: If f and g are injective, then h is injective.
ii) Disprove: If h is surjective, then f and g are surjective