Free Homework Help

Hi @Juws, I have a simple calculus problem that I can't seem the get ahold of. Maybe you can help!? Thanks in advance

Let f : Z → Z, so that f(n) = {f(n-1)/2 if f(n-1) is even, 3*(f(n-1))+1 if f(n-1) is odd}
Prove that for ∀ m ∈ Z, f(1) = m ⇒ {∃ k ∈ Z | f(k) = 1}

Example: let's look at f(1) = 3. Then we have:
f(2) = 3*3+1 = 10
f(3) = 5
f(4) = 3*5+1 = 16
f(5) = 16/2 = 8
...
f(8) = 1, which is what was postulated