Definition:Real Function/Two Variables/Substitution for y

Definition
Let $S, T \subseteq \R$ be subsets of the set of real numbers $\R$.

Let $f: S \times T \to \R$ be a (real) function of two variables:
 * $z = \map f {x, y}$

Then:
 * $\map f {x, a}$

means the real function of $x$ obtained by replacing the independent variable $y$ with $a$.

In this context, $a$ can be:
 * a real constant such that $a \in T$
 * a real function $\map g x$ whose range is a subset of $T$.