Two functions (f, g: mathbb{R} ightarrow mathbb{R}) are such that for all (x in mathbb{R}),[ g(x)=x^{2}+x+3, quad text { and }(g circ f)(x)=x^{2}-3

Two functions \(f, g: \mathbb{R} \rightarrow \mathbb{R}\) are such that for all \(x \in \mathbb{R}\),\[ g(x)=x^{2}+x+3, \quad \text { and }(g \circ f)(x)=x^{2}-3 x+5 \]

Find the possibilities for \(f\).