Real Function of Two Variables/Substitution for y/Examples/x^2 + xy^2 + 5y + 3/a

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

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

$\forall \tuple {x, y} \in \R^2: \map f {x, y} := x^2 + x y^2 + 5 y + 3$

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

Then:

\(\ds \forall x \in \R: \, \)

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

\(=\)

\(\ds x^2 + x \times a^2 + 5 \times a + 3\)

\(\ds \)

\(=\)

\(\ds x^2 + a^2 x + 5 a + 3\)

simplifying

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 $2.66 \ \text {(b)}$