Let f : N → N and g : N → N be the functions defined...

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.

Expert Solution

Colby Messinger answered 2 years ago

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Let f : N → N and g : N → N be the functions defined...

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