Fairly easy problem, but I'm stuck?

Question

#12:

Prove this conjecture:

Let f(x) be a function defined on the positive integers such that:

f(x) = x/2 if x is even
f(x) = (3*x+1)/2 if x is odd

Now I proved all the previous ones, but I need inspiration on this one. My teacher will give me extra credit on a test if i solve it, so help please!

OH sorry:

Then the conjecture is: iterates of f(x) will eventually reach 1 for any
initial value of x.

Answer 1

Where's the conjecture? You've defined f, but what about it?

Answer 2

What are we trying to prove... that this is a function?

Need more details.