Definition:Continuous Extension/Real Function

Definition
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 $f$ :
 * $\forall x \in A : f \left({x}\right) = g \left({x}\right)$