Real Function of Two Variables/Substitution for y/Examples/x + y/1 over 2

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 $\dfrac 1 2$ be substituted for $y$ in $\map f {x, y}$.

Then:

\(\ds \forall x \in \closedint {-1} 1: \, \)

\(\ds \map f {x, \dfrac 1 2}\)

\(=\)

\(\ds x + \dfrac 1 2\)

Sources

• 1963: Morris Tenenbaum and Harry Pollard: Ordinary Differential Equations ... (previous) ... (next): Chapter $1$: Basic Concepts: Lesson $2 \text C$: Function of Two Independent Variables: Example $2.67 \ \text {(a)}$