Closure in Reverse $[7$ points$]$

Suppose that $L$ is an arbitrary regular language. Prove that $L^R,$ the reverse of $L,$ is also regular.

If a string $w$ is in $L,$ the reverse of that string, $w^R,$ is in $L^R.$ The reverse operation is defined recursively as:

${}^R=$

For a string $w$ and symbol ain$,(wa{)}^R=a(w^R)$

i$.$e$.(110{)}^R=011.$