Solution
= Solution
By the <S-m-n theorem>, there is a total recursive function $h$ such that
$$
f_{h(x),1}(y)\simeq g(x,y)
$$
for all $x,y$. Apply the <recursion theorem> to $h$. It supplies an index $e$ for which
$$
f_{e,1}\simeq f_{h(e),1}.
$$
Consequently
$$
\boxed{f_{e,1}(y)\simeq g(e,y)\quad\text{for every }y\in\mathbb N.}
$$