Permutations And Combinations

Let \([t]\) be the greatest integer less than or equal to \(t\). Let \(A\) be the set of all prime factors of 2310 and \(f: A \rightarrow \mathbb{Z}\) be the function \(f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]\). The number of one-to-one functions from \(A\) to the range of \(f\) is