# Definition:Continuous Extension/Real Function

Let $A$, $B \subseteq \R$ be subsets of the real numbers such that $A \subseteq B$.
Let $f: A \to \R$ and $g: B \to \R$ be continuous real functions.
Then $g$ is a continuous extension of $f$ if and only if:
$\forall x \in A : f \left({x}\right) = g \left({x}\right)$