How to read $\langle ~\rangle$ in $\langle F(a) | a \in A \rangle$?

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In Hrbacek and Jeck's book, Introduction to set theory, the symbol $\langle~\rangle$ is introduced for function representations.

I can read $F:A \rightarrow B$, however, I can't read $\langle F(a) | a \in A \rangle $, $\langle F_a | a \in A \rangle$, $\langle F_a \rangle _{a\in A}$.

There are some examples:

$\langle 2x-1 ~|~ x ~~ real \rangle$,

$\langle x^2 ~ |~ x ~~ real \rangle$,

$\langle \frac{1}{x} ~|~ x~~real, ~~x \neq 0 \rangle$.

Each of $2x-1$, $x^2$, and $\frac{1}{x}$ is not element of set. It is some value of a function.

In the second example, when $x=1$ or $x=-1$, the value of $x^2$ are both $1$.

Can I read the second example as "the collection of all $x$ squared such that x is real"?