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

## 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 $3 \notin \closedint 1 2$.