Real Function of Two Variables/Substitution for y/Examples/x + y
Jump to navigation
Jump to search
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:
\(\ds S\) | \(:=\) | \(\ds \closedint {-1} 1\) | ||||||||||||
\(\ds T\) | \(:=\) | \(\ds \closedint 0 2\) |
Substituting $\dfrac 1 2$ for $y$
Let $\dfrac 1 2$ be substituted for $y$ in $\map f {x, y}$.
Then:
\(\ds \forall x \in \closedint {-1} 1: \, \) | \(\ds \map f {x, \dfrac 1 2}\) | \(=\) | \(\ds x + \dfrac 1 2\) |
Substituting $3$ for $y$
Let $3$ be substituted for $y$ in $\map f {x, y}$.
Then $\map f {x, 3}$ is undefined, as $3 \notin \closedint 1 2$.