I have to prove:
Family of unary partial computable functions having total computable extension is computable.
But it is not so obvious for me.
Here i provide some definitions:
If the function $h$ is obtained from the computable functions $f$ and $g$ and they are defined everywhere, then $h$ is a total function.
A function $g$ is called an extension of the function $f$ (partial function) if $Dom (f) ⊆ Dom (g)$ and $g (x) = f (x)$ for any $x ∈ Dom (f)$. Where $Dom (f)$ is the scope of function $f$.