Solution
= Solution
For $g\in G$ and $x\in\phi^{-1}(N)$,
$$
\phi(gxg^{-1})=\phi(g)\phi(x)\phi(g)^{-1}\in N,
$$
so the preimage is normal.
= Solution
For $g\in G$ and $x\in\phi^{-1}(N)$,
$$
\phi(gxg^{-1})=\phi(g)\phi(x)\phi(g)^{-1}\in N,
$$
so the preimage is normal.