Exercise 6.6.A in Foundations of Algebraic Geometry

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The exercise is "Suppose $X$ is a $\mathbb{C}$-scheme. Verify that there is a natural bijection between maps $X → \mathbb{A}_C^1$ in the category of $\mathbb{C}$-schemes and functions on $X$."

Butt directly above it in FOAG (http://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf), it states "If $X$ is a scheme, there is a bijection between the maps $X → \mathbb{A}^1$ and global sections of the structure sheaf."

Here is the confusion: what do we have to show? Isn't it immediate? I feel as if there is a subtley missing, but what?