Note that if \(X\) is polynomial time reducible to \(Y\) via \(f(x)\), then an efficient algorithm \(A\) for deciding membership in \(Y\) would also yield an efficient algorithm for deciding membership in \(X\) as follows: (i) on input \(x\), compute \(f(x)\); (ii) use \(A\) to decide if \(f(x) \in Y\), accepting if so, and rejecting if not.