Exercise 19, § 9

Let $K$ be a commutative field, $\tilde{K}$ the projective field obtained by adjoining to $K$ an infinite point (II, p. 136), $f$ and $g$ two elements of $K(X)$. Now prove that if one sets $h(X) = f(g(X))$ and if $\tilde{f}, \tilde{g}, \tilde{h}$ are the canonical extensions of $f, g, h$ to $\tilde{K}$, one has $\tilde{h} = \tilde{f} \circ \tilde{g}$.*