Two$-$Way DFA$$s

Let M be a $2$WDFA with states set $\{$i$,$ p$,$ f$\},$ start state i$,$ final state set $\{$f$\},$ input alphabet $\{$a$\},$ and transition function $\backslash$delta with $\backslash$delta $($i$,$ a$)=($f$,$ R$),\backslash$delta $($p$,$ a$)=($i$,$ R$),$ and $\backslash$delta $($f$,$ a$)=($p$,$ L$).$

Then L$($M$)$ is the set of all non$-$empty strings in a$*.$ true or false