Let $f$, $g$, and $h$ be hash functions that each map binary strings of length $2n$ to binary strings of length $n$. Suppose that $h(x) = f(g(x)||g(x))$. Prove that if $f$ and $g$ are collision resistant then $h$ is also collision resistant.
This question was asked on an earlier assignment and my professor had taken it up in class using proof by contrapositive. I am expecting a question like this to show up on our final but I have forgotten how he answered it. Could anyone off some insight into how I can answer this?