So we know that there exists a Turing Machine $M$ and a polynomial $T$ such that:
- $M$ halts on all inputs within at most $T(|x|)$ steps
- If $x$ is in $L$ then $M$ accepts $x$
- If $x$ is not in $L$ then $M$ rejects $x$
We need to show that for any other problem $L'$, there exists a polynomial time computable function $f$ such that for all $x$, $f(x)$ is in $L'$ if and only if $x$ is in $L$.
I imagine the answer is simple but I'm stumped.