The Stacks project

Exercise 111.34.10. Prove there exist a $f \in \mathbf{C}[x, t]$ which is not divisible by $t - \alpha$ for any $\alpha \in \mathbf{C}$ such that there does not exist any $Z \subset \mathop{\mathrm{Spec}}(\mathbf{C}[x, t, 1/f])$ which maps finite surjectively to $\mathop{\mathrm{Spec}}(\mathbf{C}[t])$. (I think that $f(x, t) = (xt - 2)(x - t + 3)$ works. To show any candidate has the required property is not so easy I think.)