Exercise 19, § 9

Let $K$ be a commutative field, $\tilde{K}$ the projective field obtained by adjoining to $K$ a point at infinity (no. 9) and $f$ and $g$ two elements of $K(X)$. Show that, writing $h(X) = f(g(X))$, if $\tilde{f}, \tilde{g}, \tilde{h}$ are the canonical extensions of $f, g, h$ to $\tilde{K}$, then $\tilde{h} = \tilde{f} \circ \tilde{g}$.*