According to "Elements of Set Theory" by Enderton 43p,

For a function $F$ and a point $x$ in dom $F$, the unique $y$ such that $_xF_y$ is called the

valueof $F$ at $x$ and is denoted $F(x)$. Thus $<x, F(x)>;in F$. The "$F(x)$" notation was introduced by Euler in the 1700s. We hereby resolve to use this notationonlywhen $F$ is a function and $xin dom;F$. There are, however, some artificial ways of defining $F(x)$ that are meaningful for any $F$ and $x$. For example, the set

$$bigcup{y;|<x, y>;in F}$$

is equal to $F(x)$ whenever $F$ is a function and $xin dom;F$.

I think $bigcup{y;|<x, y>;in F}$ should be ${y;|<x, y>;in F}$. What am I missing?