Real Function of Two Variables/Substitution for y/Examples/x + y/3

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Examples of Substitution for $y$ in Real Function of Two Variables

Let $\map f {x, y}$ be the real function of $2$ variables defined on the domain $S \times T$ as:

$\forall \tuple {x, y} \in S \times T: \map f {x, y} := x + y$

where $S$ and $T$ are the closed real intervals:

\(\ds S\) \(:=\) \(\ds \closedint {-1} 1\)
\(\ds T\) \(:=\) \(\ds \closedint 0 2\)

Let $3$ be substituted for $y$ in $\map f {x, y}$.

Then $\map f {x, 3}$ is undefined, as $3 \notin \closedint 1 2$.