Composition of Polynomials and Galois Theory

Question

Let $f(x)$ be a polynomial of degree $n$ over $\mathbb{Q}$, with Galois group isomorphic to the symmetric group $S_n$. How do I show that $f$ cannot be expressed as a composition $g(h(x))$ of two polynomials $g$ and $h$ of degrees > 1.

Thanks