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Let f : N ? N and g : N ? N be the functions...

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Advance Math

Let f : N ? N and g : N ? N be the functions defined as ?k ? Nf(k) = 2k and g(k) = (k/2 if k is even, (k + 1) /2 if k isodd).

(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.

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