Real Function of Two Variables/Substitution for y/Examples/x^2 + xy^2 + 5y + 3/g (x)
Jump to navigation
Jump to search
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 $\map g x$ be substituted for $y$ in $\map f {x, y}$, where $\map g x$ is a real function defined on all $\R$.
Then:
\(\ds \forall x \in \R: \, \) | \(\ds \map f {x, \map g x}\) | \(=\) | \(\ds x^2 + x \times \paren {\map g x}^2 + 5 \map g x + 3\) |
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 $2.66 \ \text {(c)}$