Let $f(x)\in \mathbb{Z}[X]$ be a polynomial of degree at least $2$.We denote the set of primes $p$ for which $f(x)$ is injective modulo $p$ as $\mathcal{T}$. Then, can we say something about the proportion of polynomials $f(x)$ for which cardinality of the set

$$\#\mathcal{P}\setminus\mathcal{T}(x)\ll \frac{x}{(\log{x})^2}.$$