In: Advanced Math
Let f : N → N and g : N → N be the functions defined as ∀k ∈ N f(k) = 2k and g(k) = (k/2 if k is even, (k + 1) /2 if k is odd).
(1) Are the functions f and g injective? surjective? bijective? Justify your answers.
(2) Give the expressions of the functions g ◦ f and f ◦ g?
(3) Are the functions g ◦ f and f ◦ g injective? surjective? bijective? Justify your answers.