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# Extension

From Mathematics Is A Science

Jump to navigationJump to searchSuppose we have sets $X$ and $Y$, a subset $A$ of $X$, and a function $f: A → Y$ on $A$. Then an *extension function* $F: X → Y$ of $f$ is any function that satisfies
$$F(x) = f(x)$$
for all $x∈A$.

In that case, the original function $f$ is the restriction $f=F|_A$ of $F$ to $A$.