Student $C$ tries to define a function $G$: $Z^{+}\rightarrow Z$ by the rule $G$($n$) = \begin{cases} \ 1, & \text{if $n$ is 1}\\ \ G(\frac{n}{2}), & \text{if $n$ is even} \\[2ex] G(3n-2), & \text{if $n$ is odd and $n>$1} \end{cases}
for all integers $n \geq $ 1. Student $D$ claims that $G$ is not well defined. Justify student $D's$ claim.
I have no idea where to begin; please can someone point me in the right direction or perhaps hints? Thank you so very much!
It is well defined if you can follow back the chain for any input $n$ and (if there are multiple routes back) if you always get the same answer. In this case the three pieces of the definition based on $n$ form a partition of $\Bbb Z^+$, so there is only one to apply at each time. If you try to evaluate $G(2^k)$, you need $G(2^{k-1})$, which needs $G(2^{k-2})$ and so on and you find it is $1$, so is well defined. But if you try to evaluate $G(3)$, you need $G(7)$, which needs $G(19)$ and you never get to a defined one, so there is not a unique value for $G(3)$