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

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: